the local langlands conjecture for gsp 4 we prove the local langlands conjecture for gsp4 f where f is a nonarchimedean local eld of characteristic zero

on the genericity of cuspidal automorphic forms of so2n 1 this is a sequel of our work js06 we extend moeglin s results m97a and m97b from the even orthogonal groups to old orthogonal groups and complete our proof of the cap conjecture for irreducible cuspidal automoprhic representations of so2n 1 a with special bessel models we also give characterization of the vanishing of the central value of the standard l function of so2n 1 a in terms of theta correspondence as result we obtain the weak langlands functorial transfer from so2n 1 a to gl2n a for irreducible cuspidal automoprhic representations of so2n 1 a with special bessel models

a method of proving non unitarity of representations of p adic groups i in this paper we exhibit a new method of proving non unitarity of representations based on semi simplicity of unitarizable representations non unitarity is proved for a half of all irreducible representations of classical p adic groups whose infinitesimal character is the same as the infinitesimal character of a generalized steinberg representation as defined in tadic am j math 120 159 210 1998 only the steinberg representation and its aubert dual are expected to be unitary here in this way we partially generalize a result of casselman to the case of classical groups our argument is completely different from casselman s argument which is hard to extend to this case it requires a very limited knowledge of the inducing cuspidal representation

a new class of particle methods particle methods are numerical methods designed to solve problems in fluid mechanics and related problems in continuum mechanics a general approach to the construction of such particle methods is presented in this article the particles are no mass points but possess a finite extension they can rotate in space and have a spin the conservation of mass is automatically guaranteed by the ansatz the forces of interaction between the particles are derived in a canonical way from the force laws of continuum mechanics and are directly based on a regularized stress tensor in the absence of external forces and of heat sources and sinks momentum angular momentum and energy are conserved as in the continuum case

on existence of generic cusp forms on semisimple algebraic groups in this paper we discuss the existence of certain classes of cuspidal automorphic representations having non zero fourier coefficients for a general semisimple algebraic group g defined over a number field k such that its archimedean group g infty is not compact when g is quasi split over k we obtain a result on existence of generic cuspidal automorphic representations which generalize results of vigneras henniart and shahidi we also discuss i the existence of cuspidal automorphic forms with non zero fourier coefficients for congruence of subgroups of g infty and ii applications related to the work of bushnell and henniart on generalized whittaker models

a particle partition of unity method for the solution of elliptic parabolic and hyperbolic pdes in this paper we present a meshless discretization technique for instationary convection diffusion problems it is based on operator splitting the method of characteristics and a generalized partition of unity method we focus on the discretization process and its quality the method may be used as an h version or a p version even for general particle distributions the convergence behavior of the different versions corresponds to that of the respective version of the finite element method on a uniform grid we discuss the implementational aspects of the proposed method furthermore we present the results of numerical examples where we considered instationary convection diffusion instationary diffusion linear advection and elliptic problems

on the ramanujan conjecture and finiteness of poles for certain l functions in this paper we prove a number of general results about automorphic l functions which appear in the constant terms of eisenstein series for an arbitrary quasi split connected reductive algebraic group over a number field these l functions were first introduced by langlands for chevalley groups 20 and through them he was led to make some of his deep conjectures 21 one significance of these l functions is that all the automorphic l functions studied so far are among them there are three general results first we obtain a uniform line of absolute convergence for all of these l functions theorem 5 1 a uniform estimate for the hecke eigenvalues of generic cusp forms on many absolutely simple quasi split connected reductive algebraic groups over number fields corollary 5 4 and an improvement on the best available estimate for the fourier coefficients of maass wave forms corollary 5 5 also follow next we establish a meromorphic continuation and functional equation for each of these l functions theorem 6 1 finally in theorem 6 2 we prove finiteness of poles on the whole complex plane for an important class of these l functions corollaries 6 6 through 6 10 more precisely let g be a quasi split connected reductive algebraic group over a number field f set g g a f where a f is the ring of adeles of f fix a borel subgroup b of g over f and let u be its unipotent radical let p be a maximal f parabolic subgroup of g with p d b in the context of the problems studied here nothing new will be obtained if one drops the maximality condition on p write p mn a levi decomposition n c u and let b u p m and n be the corresponding groups of adelic points for every place v of f let gv g fj similarly we have bv us pv me and nv let x xv be a generic character of u f u cf section 3 then each xv is generic let r ov 7tv be a cusp form on m we shall say 7t is

twisted symmetric square l functions for mathrm gl _n and invariant trilinear forms following the works of bump and ginzburg and of takeda we develop a theory of twisted symmetric square l functions for mathrm gl n we characterize their pole in terms of certain trilinear period integrals determine all irreducible summands of the discrete spectrum of mathrm gl n having nonvanishing trilinear periods and construct nonzero local invariant trilinear forms on a certain family of induced representations

a proof of langland s conjecture on plancherel measures complementary series of p adic groups analysis of p adic reductive groups our first result theorem 7 9 proves a conjecture of langlands on normalization of intertwining operators by means of local langlands root numbers and l functions at least when the group is quasi split and the inducing representation is generic assuming two natural conjectures in harmonic analysis of p adic groups we also prove the validity of the conjecture in general theorem 9 5 as our second result we obtain all the complementary series and special representations of quasi split p adic groups coming from rank one parabolic subgroups and generic supercuspidal represen

on the cohomology of compact unitary group shimura varieties at ramified split places in this article we prove results about the cohomology of compact unitary group shimura varieties at split places in nonendoscopic cases we are able to give a full description of the cohomology after restricting to integral hecke operators at p on the automorphic side we allow arbitrary ramification at p even the pel data may be ramified this gives a description of the semisimple local hasse weil zeta function in these cases we also treat cases of nontrivial endoscopy for this purpose we give a general stabilization of the expression given in 38 following the stabilization given by kottwitz in 25 this introduces endoscopic transfers of the functions h introduced in 38 we state a general conjecture relating these endoscopic transfers with langlands parameters we verify this conjecture in all cases of el type and deduce new results about the endoscopic part of the cohomology of shimura varieties this allows us to simplify the construction of galois representations attached to conjugate self dual regular algebraic cuspidal automorphic representations of gln as previously constructed by one of us 41

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

convergence of type symmetric and cut balanced consensus seeking systems we consider continuous time consensus seeking systems whose time dependent interactions are cut balanced in the following sense if a group of agents influences the remaining ones the former group is also influenced by the remaining ones by at least a proportional amount models involving symmetric interconnections and models in which a weighted average of the agent values is conserved are special cases we prove that such systems always converge we give a sufficient condition on the evolving interaction topology for the limit values of two agents to be the same conversely we show that if our condition is not satisfied then these limits are generically different these results allow treating systems where the agent interactions are a priori unknown being for example random or determined endogenously by the agent values

local coefficients as artin factors for real groups introduction the purpose of this paper is to prove the equality of certain local coefficients of arithmetic significance which were attached to representations of quasi split real reductive algebraic groups in 27 with their corresponding artin factors attached by local class field theory 21 as a consequence we establish an identity satisfied by certain normalized intertwining operators it seems to be useful in applications of the trace formula 1 29 more precisely let g be the group of real points of a quasi split reductive algebraic group over r let a be the set of simple roots defined by a fixed minimal parabolic subgroup po m0a0u of g fix 6 c a and let p p9 be the corresponding standard parabolic subgroup of g and write p man for its langlands decomposition fix a nondegenerate character x f u i a h o be an irreducible admissible x gic banach in particular x generic unitary representation of m cf section 1 given v g a the complex dual of the lie algebra of a let i v o 0 be the continuously quasi unitarily if o is unitary induced representation indp ga e v 9 and let v v o 0 be its space section 0 then f a vfoo o now let w be the weyl group of ao in g choose w g w such that w 0 c a let n be the unipotent group opposite to n define n u c wn w where w is a representative of w in g for g f a 00 define

convergence speed in distributed consensus and averaging we study the convergence speed of distributed iterative algorithms for the consensus and averaging problems with emphasis on the latter we first consider the case of a fixed communication topology we show that a simple adaptation of a consensus algorithm leads to an averaging algorithm we prove lower bounds on the worst case convergence time for various classes of linear time invariant distributed consensus methods and provide an algorithm that essentially matches those lower bounds we then consider the case of a time varying topology and provide a polynomial time averaging algorithm

on the non unitary unramified dual for classical p adic groups in this paper we give a zelevinsky type classification of unramified irreducible representations of split classical groups

consensus of quantum networks with directed interactions fixed and switching structures we study consensus seeking of quantum networks under directed balanced interactions defined by a set of permutation operators among a network of qubits the state evolution of the quantum network is described by a continuous time master equation we show that the network state always converges along the equation and the convergence limit is determined by the generating subgroup of the permutation operators we also give a tight graphical criterion regarding when such limit admits a reduced state consensus quantum consensus conditions under switching interactions are also established with the help of cut balanced consensus processes in the classical setting

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

epipelagic l packets and rectifying characters we provide an explicit construction of the local langlands correspondence for general tamely ramified reductive p adic groups and a class of wildly ramified langlands parameters furthermore we verify that our construction satisfies many expected properties of such a correspondence more precisely we show that each l packet we construct admits a parameterization in terms of the langlands dual group contains a unique generic element for a fixed whittaker datum satisfies the formal degree conjecture is compatible with central and cocentral characters provides a stable virtual character and satisfies the expected endoscopic character identities moreover we show that in the case of mathrm gl n our construction coincides with the established local langlands correspondence our techniques provide a general approach to the construction of the local langlands correspondence for tamely ramified groups and regular supercuspidal parameters

local langlands correspondence for mathrm gl _ n and the exterior and symmetric square varepsilon factors let f be a p adic field that is a finite extension of qp for some prime p the local langlands correspondence llc attaches to each continuous n dimensional semisimple representation of w f the weil deligne group for f f an irreducible admissible representation of gln f such that among other things the local l and e factors of pairs are preserved this correspondence should be robust and preserve various parallel operations on the arithmetic and analytic sides such as taking the exterior square or symmetric square in this article we show that this is the case for the local arithmetic and analytic symmetric square and exterior square e factors that is that e s 2 e s 2 and e s sym2 e s sym2 the agreement of the l functions also follows by our methods but this was already known by henniart the proof is a robust deformation argument combined with local global techniques which reduces the problem to the stability of the analytic factor s 2 under highly ramified twists when is supercuspidal this last step is achieved by relating the factor to a mellin transform of a partial bessel function attached to the representation and then analyzing the asymptotics of the partial bessel function inspired in part by the theory of shalika germs for bessel integrals the stability for every irreducible admissible representation then follows from those of the corresponding arithmetic factors as a corollary

on ergodicity infinite flow and consensus in random models we consider the ergodicity and consensus problem for a discrete time linear dynamic model driven by random stochastic matrices which is equivalent to studying these concepts for the product of such matrices our focus is on the model where the random matrices have independent but time variant distribution we introduce a new phenomenon the infinite flow and we study its fundamental properties and relations with the ergodicity and consensus the central result is the infinite flow theorem establishing the equivalence between the infinite flow and the ergodicity for a class of independent random models where the matrices in the model have a common steady state in expectation and a feedback property for such models this result demonstrates that the expected infinite flow is both necessary and sufficient for the ergodicity the result is providing a deterministic characterization of the ergodicity which can be used for studying the consensus and average consensus over random graphs

particles of variable size a problem of all particle methods is that they produce large vacuum regions when they are applied to a free gas flow for example with the approach recently proposed by the author numer math 1997 76 111 142 this difficulty can be avoided one can let the particles adapt their size to the local state of the fluid how is described in the present article the diameter as an additional degree of freedom strongly improves the performance of the numerical methods based on this particle model

a particle model of compressible fluids fluid mechanics describes the motion of mass in space under the influence of internal and external forces the particle model presented in this article is based on this fact the fluid is subdivided into a finite number of small mass packets the particles these mass packets have a finite extension and share all properties with the fluid except for the restriction that they cannot get deformed and can perform only rigid body motions the forces acting upon the particles are identical to those acting on a part of a fluid the exact conservation of mass and for the case of adiabatic flows also of entropy is automatically guaranteed by the approach when the particle size tends to zero the mean local displacement of the particles converges in the weak sense in the inviscid case the resulting flows can be regarded as solutions of the euler equations

a hamiltonian particle method for non linear elastodynamics particle methods are meshless simulation techniques in which motion of continua is approximated by discrete dynamics of a finite number of particles they have a great degree of flexibility for instance in dealing with complex large deformations or the fragmentation of solids in this paper a particle method for non linear elastodynamics of compressible and incompressible materials is developed based on a discretization of the lagrangian from which the governing equations of elastodynamics are derived using the principle of least action the discretized lagrangian leads to a finite dimensional hamiltonian system via the legendre transformation if the material is incompressible the hamiltonian system is accompanied by holonomic constraints depending on whether the material is compressible or incompressible the symplectic scheme adopted for numerical time integration is either the stormer verlet scheme or the rattle method respectively the resulting particle method inherits the symplectic structure possessed by the governing equations of elastodynamics in the case of incompressible materials incompressibility is strictly enforced at each time step some numerical tests indicate the excellence of the method for conservation of mechanical energy besides that of linear and angular momenta