direct sums of tensor products and non commutative independence abstract we point out the connection between the three known fundamental notions of non commutative independence in quantum probability and the three basic choices for forming an associative direct sum of alternating tensor products of two vector spaces

the essentially tame local langlands correspondence i 1 let f be a non archimedean local field we assume throughout that the residue field kp of f is finite of characteristic p let wp be the weil group of f formed relative to some separable algebraic closure of f for each integer n 1 let sn f be the set of equivalence classes of irreducible smooth complex representations of wp of dimension n likewise let an f be the set of equivalence classes of irreducible supercuspidal representations of the group gln f the langlands correspondence gives a bijection

supercuspidal characters of sl l over a p adic field l a prime let f be a p adic field of characteristic 0 for odd primeswith certain tameness restric tions techniques due to assem allow us to write supercuspidal characters of sl f in terms of a family of distributions defined by kazhdan following an argument of harish chandra we derive an integral formula for these distributions results of debacker and kazhdan allow us to evaluate this integral formula this in turn gives supercuspidal character formulas for sl f explicit up to the constants appearing in the gl f local character expansion our result also describes the explicit local langlands correspondence for those positive depth supercuspidal representations of gl f which do not restrict irreducibly to sl f 1 introduction in this note using techniques due to assem see 3 we derive formulas for the supercuspidal characters of sl f whereis an odd prime here f is a p adic field of characteristic 0 i e a finite extension of qp we assume p 2 although most of the time we will only need p our results illustrate some facts about supercuspidal characters which are not immediately obvious from previous work in general there is an infinite class of supercuspidal representations of gl f which decompose intoirreducible components upon restriction to sl f the character of each component then blows up near the singular set despite the fact that supercuspidal characters of gl f are bounded on regular elliptic elements near the singular set on the other hand under a certain simple condition on the order of the residue class field of f there is another infinite class of supercuspidal representations of gl f which remain irreducible upon restriction to sl f this means that the charac ters of the restrictions have the same behaviour near the singular set on sl f as on gl f in particular the characters of these supercuspidal representations of sl f are bounded on regular elliptic elements near the singular set this has also been noted in 27 the ultimate effect of this phenomenon on harmonic analysis on sl f is not yet fully understood and will be explored in future work we briefly outline the method we will use here the construction of the supercuspidal representations of gl f is completely understood it is known that all such representations are induced from open compact modulo the centre

computations of multi fluid flows abstract full numerical simulations of three dimensional flows of two or more immiscible fluids of different densities and viscosities separated by a sharp interface with finite surface tension are discussed the method used is based on a finite difference approximation of the full navier stokes equations and explicit tracking of the interface between the fluids preliminary simulations of the rayleigh taylor instability and the motion of bubbles are shown

correspondance de jacquet langlands locale et congruences modulo ell let mathrm f be a non archimedean local field of residual characteristic p and ell be a prime number different from p we consider the local jacquet langlands correspondence between ell adic discrete series of mathrm gl n mathrm f and an inner form mathrm gl m mathrm d we show that it respects the relationship of congruence modulo ell more precisely we show that two integral ell adic discrete series of mathrm gl n mathrm f are congruent modulo ell if and only if the same holds for their jacquet langlands transfers to mathrm gl m mathrm d we also prove that the langlands jacquet morphism from the grothendieck group of finite length ell adic representations of mathrm gl n mathrm f to that of mathrm gl m mathrm d defined by badulescu is compatible with reduction mod ell

a new proof of the howe conjecture let j q denote the space of g invariant distributions supported on ad g9 q if g e g set ad g f z f f g zg if q is a locally constant compactly supported function on g resp g define tq q to be the linear functional on j q defined by tq o t t 0 the set q will be fixed throughout the paper so we will abbreviate tq to t the g invariance of the distributions in j q means t ad g f t f if l is a compact open subgroup of g denote as c g l the space of compactly supported functions on g which are right l invariant similary if l is an open compact lattice in g let c g l be the space of compactly supported functions on g which are l invariant in hol howe conjectured that if q is a compact subset of g resp 9 then the restriction of the distributions in j q to c b l resp c g l is finite dimensional a more common formulation of the group version of the howe conjecture replaces the space c g l with the hecke algebra 7 g l of compactly supported l biinvariant functions on g since 7 g l c c g l apriori our formulation with c g l implies the hecke algebra formulation it is a simple matter to show that in fact the two formulations are equivalent if f e c 9 l then the function f g lf kgk 1 dk belongs to the hecke algebra and the map f 1 f is a surjection the linear functional on j q induced by f is a positive multiple of the linear functional induced by f thus the two spaces of linear functionals are equal and so the two formulations are equivalent

global jacquet langlands correspondence multiplicity one and classification of automorphic representations in this paper we generalize the local jacquet langlands correspondence to all unitary irreducible representations we prove the global jacquet langlands correspondence in characteristic zero as consequences we obtain the multiplicity one and strong multiplicity one theorems for inner forms of gl n as well as a classification of the residual spectrum and automorphic representations in analogy with results proved by m glin waldspurger and jacquet shalika for gl n

a numerical method for solving incompressible flow problems with a surface of discontinuity a numerical method for solving problems in which a moving surface of discontinuity separates regions of incompressible flow is presented the method developed is notable in that it does not introduce any artificial smoothing of the change in fluid properties across the surface of discontinuity this results in an increase in accuracy relative to methods which introduce smoothing effects the method was also shown to be fairly versatile problems describing a free surface an immiscible fluid interface and a premixed flame discontinuity were solved there is a limitation however in that the method appears to be most suitable for application to inviscid problems the reason for this limitation and possible approaches toward resolving it are discussed

free point processes and free extreme values we continue here the study of free extreme values begun in ben arous and voiculescu ann probab 34 2037 2059 2006 we study the convergence of the free point processes associated with free extreme values to a free poisson random measure voiculescu in lecture notes in mathematics springer heidelberg pp 279 349 1998 barndorff nielsen and thorbjornsen in probab theory relat fields 131 197 228 2005 we relate this convergence to the free extremal laws introduced in ben arous and voiculescu ann probab 34 2037 2059 2006 and give the limit laws for free order statistics

stable laws and domains of attraction in free probability theory in this paper we determine the distributional behavior of sums of free in the sense of voiculescu identically distributed inflnitesimal random variables the theory is shown to parallel the classical theory of independent random variables though the limit laws are usually quite difierent our work subsumes all previously known instances of weak convergence of sums of free identically distributed random variables in particular we determine the domains of attraction of stable distributions in the free theory these freely stable distributions are studied in detail in the appendix where their unimodality and duality properties are demonstrated

the levy ito decomposition in free probability in this paper we prove the free analog of the levy ito decomposition for levy processes a significant part of the proof consists of introducing free poisson random measures proving their existence and developing a theory of integration with respect to such measures the existence of free poisson random measures also yields via the free levy ito decomposition an alternative proof of the general existence of free levy processes in law

numerical simulation of premixed combustion using an enriched finite element method in this paper we present a novel discretization technique for the simulation of premixed combustion based on a locally enriched finite element method fem use is made of the g function approach to premixed combustion in which the domain is divided into two parts one part containing the burned and another containing the unburned gases a level set or g function is used to define the flame interface separating burned from unburned gases the extended finite element method x fem is employed which allows for velocity and pressure fields that are discontinuous across the flame interface lagrange multipliers are used to enforce the correct essential interface conditions in the form of jump conditions across the embedded flame interface a persisting problem with the use of lagrange multipliers in x fem has been the discretization of the lagrange multipliers in this paper the distributed lagrange multiplier technique is adopted we will provide results from a spatial convergence analysis showing good convergence however a small modification of the interface is required to ensure a unique solution finally results are presented from the application of the method to the problems of moving flame fronts the darrieus landau instability and a piloted bunsen burner flame

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

a semi lagrangean time integration approach for extended finite element methods many computational problems incorporate discontinuities that evolve in time the extendend finite element method xfem is able to represent discontinuities sharply on fixed arbitrary meshes but numerical difficulties arise if these discontinuities move in time we point out that this issue is crucial for interface problems with strongly discontinuous fields on fixed grids a method using semi lagrangean techniques is proposed to adequately handle time integration based on finite difference schemes in the context of the xfem the basic idea is to adapt previous numerical solutions to the current interface position by tracking back virtual lagrangean particles to their previous positions where an appropriate solution can be extrapo lated from a smooth field convergence properties of the proposed method in time and space are thoroughly studied for two one dimensional model problems finally the method is applied to the particularly challenging problem of premixed combustion where the discontinuity appears at the flame front separating the burnt from the unburnt gases a two dimensional and a three dimensional expanding flame demonstrates that the method is sufficiently accurate to retain the properties of the overall nitsche type formulation for interface problems with embedded strong discontinuities

a numerical method for capillarity dominant free surface flows the continuum surface force csf method has been extensively employed in the volume of fluid vof level set ls and front tracking methods to model the surface tension force it is a robust method requiring relatively easy implementation however it is known to generate spurious currents near the interface which may lead to disastrous interface instabilities and failures of grid convergence a different surface tension implementation algorithm referred to as the pressure boundary method pbm is introduced in this study the surface tension force is incorporated into the navier stokes equation via a pressure gradient while the free surface is tracked by a coupled level set and volume of fluid clsvof method it has been shown that the spurious currents are greatly reduced by the pbm method with the sharp pressure boundary condition preserved the numerical results of several test cases have been obtained and are in close agreement with data reported in the literature

noncommutative levy processes for generalized particularly anyon statistics let t mathbb r d let a function qt 2 to mathbb c satisfy q s t overline q t s and q s t 1 a generalized statistics is described by creation operators partial t dagger and annihilation operators t t in t which satisfy the q commutation relations partial s partial dagger t q s t partial dagger t partial s delta s t partial s partial t q t s partial t partial s partial dagger s partial dagger t q t s partial dagger t partial dagger s from the point of view of physics the most important case of a generalized statistics is the anyon statistics for which q s t is equal to q if s t here q in mathbb c q 1 we start the paper with a detailed discussion of a q fock space and operators partial t dagger partial t t in t in it which satisfy the q commutation relations next we consider a noncommutative stochastic process white noise omega t partial t dagger partial t lambda partial t dagger partial t t in t here lambda in mathbb r is a fixed parameter the case 0 corresponds to a q analog of brownian motion while 0 corresponds to a centered q poisson process we study q hermite q charlier respectively polynomials of infinitely many noncommutatative variables omega t t in t the main aim of the paper is to explain the notion of independence for a generalized statistics and to derive corresponding levy processes to this end we recursively define q cumulants of a field xi t t in t this allows us to define a q levy process as a field xi t t in t whose values at different points of t are q independent and which possesses a stationarity of increments in a certain sense we present an explicit construction of a q levy process and derive a nualart schoutens type chaotic decomposition for such a process

a sharp interface method for incompressible two phase flows we present a sharp interface method for computing incompressible immiscible two phase flows it couples the level set and volume of fluid techniques and retains their advantages while overcoming their weaknesses it is stable and robust even for large density and viscosity ratios on the order of 1000 to 1 the numerical method is an extension of the second order method presented by sussman m sussman a second order coupled levelset and volume of fluid method for computing growth and collapse of vapor bubbles journal of computational physics 187 2003 110 136 in which the previous method treated the gas pressure as spatially constant and the present method treats the gas as a second incompressible fluid the new method yields solutions in the zero gas density limit which are comparable in accuracy to the method in which the gas pressure was treated as spatially constant this improvement in accuracy allows one to compute accurate solutions on relatively coarse grids thereby providing a speed up over continuum or ghost fluid methods

formulas for tamely ramified supercuspidal characters of let f denote a p adic local field of residual characteristic p 3 this article gives formulas valid on the regular elliptic set for the irreducible supercuspidal characters of gl 3 f which correspond to characters of a ramified cartan subgroup in the case in which f does not contain cube roots of unity i e the case in which ramified cubic extensions of degree 3 over f cannot be galois base change results concerning simple types due to bushnell and henniart 1996 are used in the proofs

deformation spaces of one dimensional formal modules and their cohomology abstract let m m be the formal scheme which represents the functor of deformations of a one dimensional formal module over f p equipped with a level m structure by work of boyer in equal characteristic and harris and taylor the l adic etale cohomology of the generic fibre m m of m m realizes simultaneously the local langlands and jacquet langlands correspondences the proofs given so far use drinfeld modular varieties or shimura varieties to derive this local result in this paper we show without the use of global moduli spaces that the jacquet langlands correspondence is realized by the euler poincare characteristic of the cohomology under a certain finiteness assumption on the cohomology groups it is shown that the correspondence is realized in only one degree one main ingredient of the proof consists in analyzing the boundary of the deformation spaces and in studying larger spaces which can be considered as compactifications of the spaces m m

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

depth zero base change for ramified u 2 1 we give an explicit description of l packets and quadratic base change for depth zero representations of ramified unitary groups in two and three variables we show that this base change lifting is compatible with a certain lifting of families of representations of finite groups we conjecture that such a compatibility is valid in much greater generality

free stochastic measures via noncrossing partitions abstract we consider free multiple stochastic measures in the combinatorial framework of the lattice of all diagonals of an n dimensional space in this free case one can restrict the analysis to only the noncrossing diagonals we give definitions of what free multiple stochastic measures are and calculate them for the free poisson and free compound poisson processes we also derive general combinatorial ito type relationships between free stochastic measures of different orders these allow us to calculate for example free poisson charlier polynomials which are the orthogonal polynomials with respect to the free poisson measure

intertwining operators and residues i weighted characters operateurs d entrelacement normalisation groupes reels groupes p adiques representations standard les distributions j m la distribution j m x residus changements de contour les espaces 7b h ac g f s et 7b f ac g f s l application m

twisted relative trace formulae with a view towards unitary groups we introduce a twisted relative trace formula which simultaneously generalizes the twisted trace formula of langlands et al in the quadratic case and the relative trace formula of jacquet and lai certain matching statements relating this twisted relative trace formula to a relative trace formula are also proven including the relevant fundamental lemma in the biquadratic case using recent work of jacquet lapid and their collaborators and the rankin selberg integral representation of the asai l function obtained by flicker using the theory of jacquet piatetskii shapiro and shalika we give the following application let e f be a totally real quadratic extension with gal e f let u be a quasi split unitary group with respect to a cm extension m f and let u res e f u under suitable local hypotheses we show that a cuspidal cohomological automorphic representation of u whose asai l function has a pole at the edge of the critical strip is nearly equivalent to a cuspidal cohomological automorphic representation of u that is u distinguished in the sense that there is a form in the space of admitting a nonzero period over u this provides cohomologically nontrivial cycles of middle dimension on unitary shimura varieties analogous to those on hilbert modular surfaces studied by harder langlands and rapoport

non cuspidality outside the middle degree of l adic cohomology of the lubin tate tower abstract in this article we consider the representations of the general linear group over a non archimedean local field obtained from the vanishing cycle cohomology of the lubin tate tower we give an easy and direct proof of the fact that no supercuspidal representation appears as a subquotient of such representations unless they are obtained from the cohomology of the middle degree our proof is purely local and does not require shimura varieties

a level set formulation of eulerian interface capturing methods for incompressible fluid flows a level set formulation is derived for incompressible immiscible navier stokes equations separated by a free surface the interface is identified as the zero level set of a smooth function eulerian finite difference methods based on this level set formulation are proposed these methods are robust and efficient and are capable of computing interface singularities such as merging and reconnection numerical experiments are presented to demonstrate the effectiveness of the methods

the local langlands correspondence for gsp 4 over local function fields we prove the local langlands correspondence for rm gsp 4 f where f is a non archimedean local field of positive characteristic with residue characteristic 2

on limit multiplicites of discrete series representations in spaces of automorphic forms of course the groups f are then arithmetic subgroups of g in this situation it seems natural to assume that as n the spectral decomposition of l2 f g will approximate that of g in particular let 3 be a discrete series representation of g if f is a subgroup of g let re f 6 be the multiplicity of 3 in the representation of g by right translations on l2 f g choose a haar measure dg on g if f is arithmetic let v f g be the finite volume of f g for the measure induced by dg let d 3 be the formal degree of 3 for the measure dg

arbitrary lagrangian eulerian finite element analysis of free surface flow using a velocity vorticity formulation this paper describes the application of velocity vorticity formulation of the navier stokes equations for two dimensional free surface flow using an arbitrary lagrangian eulerian method the velocity poisson equations and the vorticity transport equations are solved using a finite element method to obtain the velocity and the vorticity fields in the interior region of the computational domain the boundary fitted coordinates system is adopted to solve the boundary equations for kinematic and dynamic conditions at the free surface using a finite difference method the numerical model for the velocity vorticity formulation is validated for a square cavity flow at re 400 and 1000 the solitary wave reflected from a vertical wall is chosen as a test case for comparison and validation of the free surface flow model then the proposed numerical model is used to obtain flow results for the following free surface flow cases i interaction between two opposite solitary waves ii seiche phenomenon in a rectangular reservoir and iii solitary wave through a submerged rectangular structure in a viscous fluid the efficiency of the present numerical model for numerical treatment of free surface flows is discussed furthermore the advantage of this formulation with respect to primitive variables formulation is addressed from the computational point of view

an explicit matching theorem for level zero discrete series of unit groups of p adic simple algebras for a f a central simple algebra over a p adic local field the group of units a glm dd is a general linear group over a central division algebra dd f of index d the product n dm being fixed the abstract matching theorem amt implies the existence of bijective maps jl between the sets of discrete series representations of the groups a such that a character relation is preserved in this paper we construct maximal level zero extended type components for every level zero discrete series representation of a its maximal level zero extended type determines the discrete series representation uniquely without any twist ambiguities as for the usual types and conversely every level zero discrete series representation contains a maximal level zero extended type component which is unique up to conjugacy in order to determine how jl matches the extended types we find certain regular elliptic elements where the characters of and are the same and we compute the character values at these elements by using a version of shintani descent which we develop in appendix b surprisingly we find that amt also implies explicit shintani descent for irreducible characters of finite general linear groups which have cuspidal descent named author let f be a locally compact p adic field let dd be a central division algebra of index d over f and let a mm dd the algebra of all m m matrices with entries in dd then a is a central simple f algebra of reduced degree n dm and the group of units a of a is the group of f points of a connected reductive algebraic group defined over f the group a is separable totally disconnected and unimodular and the harmonic analysis of a as is well known is linked to numerous problems in arithmetic it is interesting and perhaps may be regarded as a version of the abstract matching theorem amt see 0 2 that the representation theory of a depends upon the parameters d m associated to a but not more specifically on the isomorphism class of a we follow the convention of writing dd for any central f division algebra of index d we also write dn for any one of the n isomorphism class representatives of central f division algebras of index n 1991 mathematics subject classification 22e50 1the work reported in this paper grew out of a research in pairs sojourn at the mathematisches institut oberwolfach the authors wish to express their appreciation to the institut for its support of their research as well as for an enjoyable stay at the institut

semicircular limits on the free poisson chaos counterexamples to a transfer principle we establish a class of sufficient conditions ensuring thata sequence of multiple integrals with respect to a free poisson measure converges to a semicircular limit we use this result to construct a set of explicit counterexamples showing that the transfer principle between classical and free brownian motions recently proved by kemp nourdin peccati and speicher 2012 does not extend to the framework of poisson measures our counterexamples implicitly use kernels appearing in the classical theory of random geometric graphs several new results of independent interest are obtained as necessary steps in our analysis in particu lar i a multiplication formula for free poisson multiple integrals ii diagram formulae and spectral bounds for these objects and iii a counterexample to the general universality of the gaussian wiener chaos in a classical setting

orbital integrals on p adic groups a proof of the howe conjecture let g be a connected reductive group over a p adic field f of characteristic 0 let g g f let o be a compact subset of g og the invariant subset gxg1 g e g x e co of g we say that a closed invariant subset of g q is compact modulo conjugation if q c wg for some compact co it is equivalent to assume that the traces of q on all cartan subgroups of g are compact the purpose of this article is to prove the following theorem concerning invariant distributions on g which had been conjectured by howe 10 let of q denote the set of invariant distributions supported in u if k is a compact open subgroup of g let xk be the hecke algebra of compactly supported functions on g with complex values invariant on the left and right by k

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

addition of certain non commuting random variables soit g le groupe libre non commutatif sur deux generateurs et soit u j j 1 2 les unites dans l 2 g correspondant a la translation a gauche par les generateurs et on considere l 2 g la fonction g g e soient x j des operateurs de la forme x j j u j les operateurs x j peuvent etre consideres comme des variables aleatoires de moments ou de facon equivalente avec des distributions donnees par les fonctionnelles analytiques j ou j f avec ces conventions la distribution de x 1 x 2 depend seulement des distributions de x 1 et x 2 on explique cette relation

fourier transform and the global gan gross prasad conjecture for unitary groups by the relative trace formula approach of jacquet rallis we prove the global gan gross prasad conjecture for unitary groups under some local restrictions for the automorphic representations

a high order projection method for tracking fluid interfaces in variable density incompressible flows we present a numerical method for computing solutions of the incompressible euler or navier stokes equations when a principal feature of the flow is the presence of an interface between two fluids with different fluid properties the method is based on a second order projection method for variable density flows using an approximate projection formulation the boundary between the fluids is tracked with a second order volume of fluid interface tracking algorithm we present results for viscious rayleigh taylor problems at early time with equal and unequal viscosities to demonstrate the convergence of the algorithm we also present computational results for the rayleigh taylor instability in air helium and for bubbles and drops in an air water system without surface tension to demonstrate the behavior of the algorithm on problems with large density and viscosity contrasts

the immersed interface method for the navier stokes equations with singular forces abstract peskin s immersed boundary method has been widely used for simulating many fluid mechanics and biology problems one of the essential components of the method is the usage of certain discrete delta functions to deal with singular forces along one or several interfaces in the fluid domain however the immersed boundary method is known to be first order accurate and usually smears out the solutions in this paper we propose an immersed interface method for the incompressible navier stokes equations with singular forces along one or several interfaces in the solution domain the new method is based on a second order projection method with modifications only at grid points near or on the interface from the derivation of the new method we expect fully second order accuracy for the velocity and nearly second order accuracy for the pressure in the maximum norm including those grid points near or on the interface this has been confirmed in our numerical experiments furthermore the computed solutions are sharp across the interface nontrivial numerical results are provided and compared with the immersed boundary method meanwhile a new version of the immersed boundary method using the level set representation of the interface is also proposed in this paper

trace paley wiener theorem in the twisted case a version of the trace paley wiener theorem for a reductive padic group in the context of twisted harmonic analysis with respect to an outer automorphism is proved let g be a connected reductive algebraic group over a p adic field f of characteristic 0 and let g g f let po be a minimal parablic subgroup of g let e be an outer automorphism of g of finite order r of g and suppose that e fixes po elements x y e g are called e conjugate if y g 1xe g for some g e g a distribution on g which is invariant under twisted conjugacy is called e invariant the objects of study in twisted harmonic analysis are e invariant distributions the main examples are provided by twisted orbital integrals invariant integrals over twisted conjugacy classes and by twisted characters which are obtained as follows let ir be an irreducible admissible representation of g and let e 7r denote the representation of g through which g e g acts by r e 1 g if 7r is equivalent to e ir then there exists an operator 7r e unique up to rth roots of unity such that 7r e 7r g 7r e 1 7r e g and ir e r 1 in other words 7r extends to the semidirect product g c x e the twisted character of ir which depends on the choice of ir e is the distribution f tr ir f ir e on the space 1 g of compactly supported locally constant functions on g in applications of the trace formula to global problems in the theory of automorphic representations it is often necessary to use results on the representation theory and harmonic analysis of reductive groups over p adic fields because of the role played by twisted local harmonic analysis in applications of the twisted trace formula e g 1 10 it is important to have available extensions to the twisted case of results known for ordinary harmonic analysis many results in harmonic analysis extend to the twisted case for example by 7 harish chandra s theorem on the local integrability of characters holds for twisted characters the purpose of this paper is to prove a twisted version proposition 11 2 of the trace paley wiener theorem for p adic groups of bernstein deligne and kazhdan given in 3 the twisted paley wiener theorem gives a characterization of functions of the form ir tr ir f i e for some f e g in 1 6 the appropriate setting for the twisted theorem is developed in 710 results needed for the proof of proposition 11 2 are proved propositioii 7 4 is a twisted version of casselman s theorem on characters the proof of proposition 11 2 follows the plan of the argument given in 3 with modifications for the twisted received by the editors december 12 1986 and in revised form june 11 1987 1980 mathematics subject classification 1985 revision primary 22e50 the author was partially supported by grants from the national science foundation and the sloan foundation e 1988 american mathematical society 0002 9947 88 1 00 25 per page

resolutions for representations of reductive p adic groups via their buildings schneider stuhler and vigneras have used cosheaves on the affine bruhat tits building to construct natural projective resolutions of finite type for admissible representations of reductive p adic groups in characteristic not equal to p we use a system of idempotent endomorphisms of a representation with certain properties to construct a cosheaf and a sheaf on the building and to establish that these are acyclic and compute homology and cohomology with these coefficients this implies bernstein s result that certain subcategories of the category of representations are serre subcategories furthermore we also get results for convex subcomplexes of the building following work of korman this leads to trace formulas for admissible representations

ripple a new model for incompressible flows with free surfaces a new free surface flow model ripple is summarised ripple obtains finite difference solutions for incompressible flow problems having significant surface tension forces at free surfaces of arbitrarily complex topology the key innovation is the continuum surface force model which represents surface tension as a localised volume force other features include a higher order momentum advection model a volume of fluid free surface treatment and an efficient two step projection solution method ripple s unique capabilities are illustrated with two example problems low gravity jet induced tank flow and the collision and coalescence of two cylindrical rods

on the k0 of a p adic group this article deals with various topics related with grothendieck groups invariant distributions parabolic and compact inductions for a p adic group g the main result is a description of the k0 of the hecke algebra of g in terms of discrete series of levi subgroups which has an interesting behavior with regard to parabolic restriction and induction a similar description but no more compatible with these parabolic functors is obtained for overline mathcal h and the hattori rank map gets an easy description in this dictionary we follow a beautiful idea of j bernstein consisting in comparing two natural filtrations on these objects one of combinatorial nature and one of topological nature the combinatorial filtrations are related to the structure of levi subgroupsin g and have counterparts concerning many classical objects of interest as the grothendieck group of finite length g modules r g the set sr of regular semi simple conjugacy classes and the variety g of infinitesimal characters these filtrations will turn out to be compatible in a sense to be specified with regard to all the classical operations or morphisms between these objects

a continuum method for modeling surface tension abstract a new method for modeling surface tension effects on fluid motion has been developed interfaces between fluids of different properties or colors are represented as transition regions of finite thickness across which the color variable varies continuously at each point in the transition region a force density is defined which is proportional to the curvature of the surface of constant color at that point it is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero the continuum method eliminates the need for interface reconstruction simplifies the calculation of surface tension enables accurate modeling of two and three dimensional fluid flows driven by surface forces and does not impose any modeling restrictions on the number complexity or dynamic evolution of fluid interfaces having surface tension computational results for two dimensional flows are given to illustrate the properties of the method

theorie de lubin tate non abelienne et representations elliptiques non abelian lubin tate theory studies the cohomology of some moduli spaces for p divisible groups the broadest definition of which is due to rapoport zink aiming both at providing explicit realizations of local langlands functoriality and at studying bad reduction of shimura varieties in this paper we consider the most famous examples the so called drinfeld and lubin tate towers in the lubin tate case harris and taylor proved that the supercuspidal part of the cohomology realizes both the local langlands and jacquet langlands correspondences as conjectured by carayol recently boyer computed the remaining part of the cohomology and exhibited two defects first the representations of gl d which appear are of a very particular and restrictive form second the langlands correspondence is not realized anymore in this paper we study the cohomology complex in a suitable equivariant derived category and show how it encodes langlands correspondence for elliptic representations then we transfer this result to the drinfeld tower via an enhancement of a theorem of faltings due to fargues we deduce that deligne s weight monodromy conjecture is true for varieties uniformized by drinfeld s coverings of his symmetric spaces this completes the computation of local l factors of some unitary shimura varieties

a boundary condition capturing method for incompressible flame discontinuities abstract in this paper we propose a new numerical method for treating two phase incompressible flow where one phase is being converted into the other e g the vaporization of liquid water we consider this numerical method in the context of treating discontinuously thin flame fronts for incompressible flow this method was designed as an extension of the ghost fluid method 1999 j comput phys 152 457 and relies heavily on the boundary condition capturing technology developed in liu et al 2000 j comput phys 154 15 for the variable coefficient poisson equation and in kang et al in press j comput phys for multiphase incompressible flow our new numerical method admits a sharp interface representation similar to the method proposed in helenbrook et al 1999 j comput phys 148 366 since the interface boundary conditions are handled in a simple and straightforward fashion the code is very robust e g no special treatment is required to treat the merging of flame fronts the method is presented in three spatial dimensions with numerical examples in one two and three spatial dimensions

a construction of the supercuspidal representations of _ adic let f be a nondiscrete locally compact non archimedean field in this paper we construct all irreducible supercuspidal representations of g gl n f for each such representation which we may as well assume is unitary we give a subgroup j of g that is compact mod the center z of g and a finite dimensional representation of j such that inducing to g gives the proof that all supercuspidals have been constructed appeals to a theorem the matching theorem that has been proved by global methods

a new high order immersed interface method for solving elliptic equations with imbedded interface of discontinuity this paper presents a new high order immersed interface method for elliptic equations with imbedded interface of discontinuity compared with the original second order immersed interface method of r j leveque z li the immersed interface method for elliptic equations with discontinuous coefficients and singular sources siam j numer anal 31 1994 1001 25 the new method achieves arbitrarily high order accuracy for derivatives at an irregular grid point by imposing only two physical jump conditions together with a wider set of grid stencils the new interface difference formulas are expressed in a general explicit form so that they can be applied to different multi dimensional problems without any modification the new interface algorithms of up to o h 4 accuracy have been derived and tested on several one and two dimensional elliptic equations with imbedded interface compared to the standard second order immersed interface method the test results show that the new fourth order immersed interface method leads to a significant improvement in accuracy of the numerical solutions the proposed method has potential advantages in the application to two phase flow because of its high order accuracy and simplicity in applications

geometric approach to the local jacquet langlands correspondence in this paper we give a purely geometric approach to the local jacquet langlands correspondence for rm gl n over a p adic field under the assumption that the invariant of the division algebra is 1 n we use the ell adic etale cohomology of the drinfeld tower to construct the correspondence at the level of the grothendieck groups with rational coefficients moreover assuming that n is prime we prove that this correspondence preserves irreducible representations this gives a purely local proof of the local jacquet langlands correspondence in this case we need neither a global automorphic technique nor detailed classification of supercuspidal representations of rm gl n

a front tracking method for viscous incompressible multi fluid flows abstract a method to simulate unsteady multi fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described the flow field is discretized by a conservative finite difference approximation on a stationary grid and the interface is explicitly represented by a separate unstructured grid that moves through the stationary grid since the interface deforms continuously it is necessary to restructure its grid as the calculations proceed in addition to keeping the density and viscosity stratification sharp the tracked interface provides a natural way to include surface tension effects both two and three dimensional full numerical simulations of bubble motion are presented

on central critical values of the degree four l functions for text gsp left 4 right a simple trace formula we establish a simple relative trace formula for text gsp 4 and inner forms with respect to bessel subgroups to obtain a certain bessel identity from such an identity one can hope to prove a formula relating central values of degree four spinor l functions to squares of bessel periods as conjectured by bocherer under some local assumptions we obtain nonvanishing results i e a global gross prasad conjecture for text so 5 text so 2

cyclic homology and the selberg principle abstract an abstract selberg principle is proved for a smooth compactly supported function f on a connected reductive p adic group which is the trace of some idempotent n n matrix this selberg principle states that the orbital integral of f relative to a non compact element vanishes this generalizes the work of julg and valette who treated the rank one case versions of the abstract selberg principle are proved also for finite groups and for discrete groups computations of the hochschild and cyclic homology of the convolution algebra of compactly supported functions are given

a fixed grid sharp interface method for bubble dynamics and phase change abstract a numerical method has been developed for direct simulation of bubble dynamics with large liquid to vapor density ratio and phase change the numerical techniques are based on a fixed grid finite volume method capable of treating the interface as a sharp discontinuity the unsteady axisymmetric navier stokes equations and energy equation in both liquid and vapor phases are computed the mass momentum and energy conditions are explicitly matched at the phase boundary to determine the interface shape and movement the cubic b spline is used in conjunction with a fairing algorithm to yield smooth and accurate information of curvatures nondimensional parameters including reynolds weber and jakob numbers are varied to offer insight into the physical and numerical characteristics of the bubble dynamics based on the present sharp interface approach bubble dynamics for density ratio of 1600 or higher with and without phase change can be successfully computed

on some constants in the supercuspidal characters of operatorname gl _l l a prime neq p the article gives explicit values of some constants which appear in the character formula for the irreducible supercuspidal representation of gl l f for f a local field of the residual characteristic p i

a new example of independence and white noise we examine the notion of free independence according to voiculescu this form of independence is used for defining free white noise or process with stationary and freely independent increments we prove a general limit theorem giving the combinatorics of infinitely freely divisible states and thus of free white noises with the help of admissible partitions we realize the free analogues of the wiener process and of the poisson process as processes on the full fock space ofl2