godement jacquet l functions and full theta lifts we relate poles of local godement jacquet l functions to distributions on matrix spaces with singular supports as an application we show the irreducibility of the full theta lifts to mathrm gl n mathrm f of generic irreducible representations of mathrm gl n mathrm f where mathrm f is an arbitrary local field

unitary shimura correspondences for split real groups we find a relationship between certain complementary series representations for nonlinear coverings of split simple groups and spherical complementary series for different linear groups the main technique is barbasch s method of calculating some intertwining operators purely in terms of the weyl group

on the langlands functoriality for automorphic forms this is the extended notes of my lcctures on the langlands functoriality of automorphic forms which are in particular on the topics closely related to my recent work

the price of anarchy of affine congestion games with similar strategies abstract affine congestion games are a well studied model for selfish behavior in distributed systems such as transportation and communication networks seminal influential papers in algorithmic game theory have bounded the worst case inefficiency of nash equilibria termed as price of anarchy in several variants of these games in this work we investigate to what extent these bounds depend on the similarities among the players strategies our notion of similarity is modeled by assuming that given a parameter 1 the costs of any two strategies available to a same player when evaluated in absence of congestion are within a factor one from the other it turns out that for the non atomic case better bounds can always be obtained for any finite value of for the atomic case instead 3 2 and 2 are necessary and sufficient conditions to obtain better bounds in games played on general graph topologies and on parallel link graphs respectively it is worth noticing that small values of model the behavioral attitude of players who are partially oblivious to congestion and are not willing to significantly deviate from what is their best strategy in absence of congestion

matroids are immune to braess paradox the famous braess paradox describes the counterintuitive phenomenon in which in certain settings an increase of resources such as a new road built within a congested network may in fact lead to larger costs for the players in an equilibrium in this paper we consider general nonatomic congestion games and give a characterization of the combinatorial property of strategy spaces for which the braess paradox does not occur in short matroid bases are precisely the required structure we prove this characterization by two novel sensitivity results for convex separable optimization problems over polymatroid base polyhedra which may be of independent interest

integer linear programs and local search for max cut the paper deals with the complexity of the local search a topic introduced by johnson papadimitriou and yannakakis one consequence of their work and a recent paper by schaffer and yannakakis is that the local search does not provide a polynomial time algorithm to find locally optimum solutions for several hard combinatorial optimization problems this motivates us to seek easier instances for which the local search is polynomial in particular it has been proved recently by schaffer and yannakakis that the max cut problem with the flip neighborhood is pls complete and hence belongs among the most difficult problems in the pls class polynomial time local search the flip neighborhood of a 2 partition is defined by moving a single vertex to the opposite class we prove that when restricted to cubic graphs the flip local search becomes easy and finds a local max cut in o n 2 steps to prove the result we introduce a class of integer linear programs associated with cubic graphs and provide a combinatorial characterization of their feasibility

differential operators on homogeneous spaces iii characteristic varieties of harish chandra modules and of primitive ideals letg be a semi simple complex algebraic group with lie algebra and flag varietyx g b for each primitive idealj with trivial central character in the enveloping algebrau we define a characteristic variety in the cotangent bundle ofx which projects under the springer resolution mapt x onto the closure of a nilpotent orbit we prove that this characteristic variety is theg saturation of the characteristic variety of a highest weight module with annihilatorj we conjecture that it is irreducible forg sl n our conjecture would provide a geometrical explanation for the classification of primitive ideals in terms of weyl group representations as achieved by a joseph the presentation of these ideas here is simultaneously used to some extent as an opportunity to continue our more general systematic discussion of differential operators on a complete homogeneous space and to study more generally characteristic varieties of harish chandra modules

on the voronoi formula for gl n we prove a general vorono u i formula for cuspidal automorphic representations of rm gl n over number fields this generalizes recent work by miller schmid and goldfeld li on maass forms our method follows closely the adelic framework of integral representations of l functions the proof is flexible enough to allow ramification and we propose possible variants for example the assumption that the additive twist is trivial at places where the representation is ramified is sufficient to obtain an explicit final statement with hyper kloosterman sums

unitary representations induced from maximal parabolic subgroups abstract it is known that the problem of classifying the irreducible unitary representations of a linear connected semisimple lie group g comes down to deciding which langlands quotients j man v are infinitesimally unitary here man is any cuspidal parabolic subgroup is any discrete series or nondegenerate limit of discrete series representation of m and v is any complex valued linear functional on the lie algebra of a satisfying certain positivity and symmetry properties the authors determine which langlands quotients are infinitesimally unitary under the conditions that g is simple that dim a 1 and that g is neither split f 4 nor split g 2

intrinsic robustness of the price of anarchy the price of anarchy defined as the ratio of the worst case objective function value of a nash equilibrium of a game and that of an optimal outcome quantifies the inefficiency of selfish behavior remarkably good bounds on this measure are known for a wide range of application domains however such bounds are meaningful only if a game s participants successfully reach a nash equilibrium this drawback motivates inefficiency bounds that apply more generally to weaker notions of equilibria such as mixed nash equilibria and correlated equilibria and to sequences of outcomes generated by natural experimentation strategies such as successive best responses and simultaneous regret minimization we establish a general and fundamental connection between the price of anarchy and its seemingly more general relatives first we identify a canonical sufficient condition for an upper bound on the price of anarchy of pure nash equilibria which we call a smoothness argument second we prove an extension theorem every bound on the price of anarchy that is derived via a smoothness argument extends automatically with no quantitative degradation in the bound to mixed nash equilibria correlated equilibria and the average objective function value of every outcome sequence generated by no regret learners smoothness arguments also have automatic implications for the inefficiency of approximate equilibria for bicriteria bounds and under additional assumptions for polynomial length best response sequences third we prove that in congestion games smoothness arguments are complete in a proof theoretic sense despite their automatic generality they are guaranteed to produce optimal worst case upper bounds on the price of anarchy

small unitary representations of the double cover of sl m the irreducible unitary representations of the double cover sl m of the real group sl m with infinitesimal character p which are small in the sense that their annihilator in the universal enveloping algebra is maximal are expressed as langlands quotients of generalized principal series in the case where m is even we show that there are four such representations and in the case where m is odd there is just one the representations smallness allows them to be written as a sum of virtual representations leading to a character formula for their k types we investigate the place of these small representations in the orbit method and in the case of sl 2l 1 show that the representation is attached to a nilpotent coadjoint orbit the k type spectrum for the langlands quotients is explicitly determined and shown to be multiplicity free

locality in distributed graph algorithms this paper concerns a number of algorithmic problems on graphs and how they may be solved in a distributed fashion the computational model is such that each node of the graph is occupied by a processor which has its own id processors are restricted to collecting data from others which are at a distance at most t away from them in t time units but are otherwise computationally unbounded this model focuses on the issue of locality in distributed processing namely to what extent a global solution to a computational problem can be obtained from locally available data three results are proved within this model a 3 coloring of an n cycle requires time omega log n this bound is tight by previous work of cole and vishkin any algorithm for coloring the d regular tree of radius r which runs for time at most 2r 3 requires at least omega sqrt d colors in an n vertex graph of largest degree delta an o delta 2 coloring may be found in time o log n

simple local search problems that are hard to solve many algorithms for np hard optimization problems find solutions that are locally optimal in the sense that the solutions cannot be improved by a polynomially computable perturbation very little is known about the complexity of finding locally optimal solutions either by local search algorithms or using other indirect methods johnson papadimitriou and yannakakis j comput system sci 37 1988 pp 79 100 studied this question by defining a complexity class pls that captures local search problems it was proved that finding a partition of a graph that is locally optimal into equal parts with respect to the acclaimed kernighan lin algorithm is pls complete it is shown here that several natural simple local search problems are pls complete and thus just as hard two examples are finding a partition that cannot be improved by a single swap of two vertices and finding a stable configuration for an undirected connectionist network when edges or other objects are unweighted then a local optimum

induction automorphe pour gl n c for f r or c isomorphism classes of irreducible g k modules for gl n f are parametrized by n dimensional representations of the weil group wf of f we can induce to wr a representation of wc which has index 2 in wr that gives a process of automorphic induction which to an irreducible g k module for gl n c associates an irreducible g k module c r for gl 2n r in the present paper we show that if is unitary and generic then is determined by up to isomorphism via a character identity entirely analogous to the character identity occurring in the automorphic induction process for p adic fields this completes the theory of automorphic induction for local and global representations of gl n over number fields

all sl 3 r ladder representations all unitary and nonunitary ladder multiplicity free with respect to the so 3 maximal compact subgroup representations of the double covering group sl 3 r of the sl 3 r group are cataloged and presented explicitly the list of nonunitary representations is corrected and completed and a new insight concerning the j 2 ladder representation starting with j 3 2 is obtained

nilpotent orbits normality and hamiltonian group actions the theory of coadjoint orbits of lie groups is central to a number of areas in mathematics a list of such areas would include 1 group representation theory 2 symmetry related hamiltonian mechanics and attendant physical theories 3 symplectic geometry 4 moment maps and 5 geometric quantization from many points of view the most interesting cases arise when the group g in question is semisimple for semisimple g the most familiar of the orbits are orbits of semisimple elements in that case the associated representation theory is pretty much understood the borel weil bott theorem and noncompact analogs e g zuckerman functors the isotropy subgroups are reductive and the orbits are in one form or another related to flag manifolds and their natural generalizations a totally different experience is encountered with nilpotent orbits of semisimple groups here the associated representation theory unipotent representations is poorly understood and there is a loss of reductivity of isotropy subgroups to make matters worse or really more interesting orbits are no longer closed and there can be a failure of normality for orbit closures in addition simple connectivity is generally gone but more seriously there may exist no invariant polarizations the interest in nilpotent orbits of semisimple lie groups has increased sharply over the last two decades this perhaps may be attributed to the recurring experience that sophisticated aspects of semisimple group theory often lead one to these orbits e g the springer correspondence with representations of the weyl group this paper presents new results concerning the symplectic and algebraic geometry of the nilpotent orbits 0 and the symmetry groups of that geometry the starting point is the recognition made also by others that the ring r of regular functions on any g homogeneous cover m of 0 is not only a poisson algebra the case for any coadjoint orbit but that r is also naturally graded the key theme is that the same nilpotent orbit may be shared by more than one simple group the key result is the determination of all pairs of simple lie groups having a shared nilpotent orbit furthermore there is then a unique maximal such group and this group is encoded in the symplectic and algebraic

convergence and approximation in potential games we study the speed of convergence to approximately optimal states in two classes of potential games we provide bounds in terms of the number of rounds where a round consists of a sequence of movements with each player appearing at least once in each round we model the sequential interaction between players by a best response walk in the state graph where every transition in the walk corresponds to a best response of a player our goal is to bound the social value of the states at the end of such walks in this paper we focus on two classes of potential games selfish routing games and cut games or party affiliation games fabrikant et al 2004 12 other than bounding the price of anarchy of selfish routing games roughgarden and tardos 2002 25 awerbuch et al 2005 2 christodoulou and koutsoupias 2005 9 there are many interesting problems about game dynamics in these games it is known that exponentially long best response walks may exist to pure nash equilibria fabrikant et al 2004 12 and random best response walks converge to solutions with good approximation guarantees after polynomially many best responses goemans et al 2005 17 in this paper we study the speed of convergence on deterministic best response walks in these games and prove that starting from an arbitrary configuration after one round of best responses of players the resulting configuration is a q n approximate solution furthermore we show that starting from an empty configuration the solution after any round of best responses is a constant factor approximation we also provide a lower bound for the multi round case where we show that for any constant number of rounds t the approximation guarantee cannot be better than n e t for some e t 0 we also study cut games that provide an illustrative example of potential games the convergence of potential games to locally optimum solutions has been studied in the context of local search algorithms johnson et al 1988 19 schaffer and yannakakis 1991 28 in these games we consider two social functions the cut defined as the weight of the edges in the cut and the total happiness defined as the weight of the edges in the cut minus the weight of the remaining edges for the cut social function we prove that the expected social value after one round of a random best response walk is at least a constant factor approximation to the optimal social value we also exhibit exponentially long best response walks with poor social value for the unweighted version of this cut game we prove w n and o n lower and upper bounds on the number of rounds of best responses to converge to a constant factor cut in addition we suggest a way to modify the game to enforce a fast convergence in any fair best response walk for the total happiness social function we show that for unweighted graphs of sufficiently large girth starting from a random configuration greedy behavior of players in a random order converges to an approximate solution after one round

on howe s duality theorem abstract we adopt the langlands classification to the context of real reductive dual pairs and prove that howe s duality correspondence maps hermitian representations to hermitian representations

existence of klyachko models for gl n r and gl n c we prove that any irreducible unitary representation of gl n r and gl n c admits an equivariant linear form with respect to one of the subgroups considered by klyachko

price of anarchy and an approximation algorithm for the binary preference capacitated selfish replication game abstract we consider the capacitated selfish replication csr game with binary preferences over general undirected networks we study the price of anarchy of such games and show that it is bounded above by 3 we develop a quasi polynomial algorithm o n 2 ln d where n is the number of players and d is the diameter of the network which can find in a distributed manner an allocation profile that is within a constant factor of the optimal allocation and hence of any pure strategy nash equilibrium ne of the game proof of this result uses a novel potential function we further show that when the underlying network has a tree structure every globally optimal allocation is an ne which can be reached in only linear time we formulate the optimal solutions and ne points of the csr game using integer linear programs finally we introduce the lcsr game as a localized version of the csr game wherein the actions of the players are restricted to only their close neighborhoods

covariants of spn c and degenerate principal series of gln h let m n and let p m2n m slm be the algebra of all slm c invariant polynomials on the space m2n m of all 2n m complex matrices we determine the free generators of its subalgebra of spn c covariants these generators are given as pfaffians they are used to study the degenerate principal series representations of gln h induced from characters of a maximal parabolic subgroup we determine the composition series and unitarity of these representations

the unitary dual for complex classical lie groups in this paper we classify the unitary spectrum of the complex classical groups let g be any complex simply connected semisimple lie group there are two well known ways of constructing unitary representations from lower groups unitary induction from a parabolic subgroup and complementary series a reasonable way to describe the unitary dual is to find a distinguished set of representations for each group such that every other unitary representation is obtained from this set by the above constructions from strictly smaller parabolic subgroups this is entirely similar to the classification of admissible modules where the distinguished representations are the discrete series for integral infinitesimal character such a set is provided by the special unipotent representations introduced in bv1 their existence and unitarity was conjectured earlier by a they were shown to have many interesting properties such as the fact that their annihilator is a maximal primitive ideal from this it was possible to obtain character formulas for them however it is clear that this set is not large enough to describe the entire unitary spectrum for example in type c the metaplectic representation is not special unipotent or even one of the larger class of representations considered in a the definition of special unipotent representations suggests that one should consider representations with maximal primitive ideal and infinitesimal character as small as possible it is not clear which of them should be unitary imposing the condition that the annihilator be a completely prime ideal which is necessary for unitarity does not seem to be very helpful either thus one is left with the task of explicitly computing the g invariant form and ruling out the cases when it is indefinite this is an almost impossible calculation a rough estimate says that one needs to compute signatures on the k types in the principal series which have length ii 2p ql

the complexity of the lin kernighan heuristic for the traveling salesman problem it is shown that finding a local optimum solution with respect to the lin kernighan heuristic for the traveling salesman problem is pls complete and thus as hard as any local search problem

computation and efficiency of potential function minimizers of combinatorial congestion games we study the computation and efficiency of pure nash equilibria in combinatorial congestion games where the strategies of each player i are given by the binary vectors of a polytope p i our main goal is to understand which structural properties of such polytopal congestion games enable us to derive an efficient equilibrium selection procedure to compute pure nash equilibria with attractive social cost approximation guarantees to this aim we identify two general properties of the underlying aggregation polytope p n sum i p i which are sufficient for our results to go through namely the integer decomposition property idp and the box totally dual integrality property box tdi our main results for polytopal congestion games satisfying idp and box tdi are as follows i we show that pure nash equilibria can be computed in polynomial time in fact we obtain this result through a general framework for separable convex function minimization which might be of independent interest ii we bound the inefficiency of these equilibria and show that this provides a tight bound on the price of stability iii we also prove that these results extend to strong equilibria for the bottleneck variant of polytopal congestion games examples of polytopal congestion games satisfying idp and box tdi include common source network congestion games symmetric totally unimodular congestion games non symmetric matroid congestion games and symmetric matroid intersection congestion games in particular r arborescences and strongly base orderable matroids

howe correspondence for real unitary groups roger howe proved that for any reductive dual pair g g in the symplectic groupsp 2n r there is a one to one correspondence of irreducible admissible representations of some two fold covers ofgandg we determine this correspondence explicitly for dual pairs of the form u p q u r s withr s p q and describe it in terms of langlands parameters in this case the correspondence may be understood in a natural way as a correspondence of representations of the linear groups rather than the appropriate covers we show that every irreducible admissible representation ofu p q occurs in the correspondence with precisely one unitary group of equal rank this result verifies a conjecture of harris kudla and sweet who investigated the correspondence for unitary groups of equal size overp adic fields the correspondence of discrete series representations was determined by j s li for induced representations the correspondence is obtained in a natural way from the corresponding discrete series on the respective levi factors of the parabolic subgroups ofu p q andu r s generalizing a result of li we show that under the correspondence representations with nonzero cohomology are matched in an interesting way with unitarity not necessarily preserved the proof uses the induction principle which is due to kudla and an argument involvingk types and the space of joint harmonics howe

extremal cuts of sparse random graphs for erd s renyi random graphs with average degree and uniformly random regular graph on nn vertices we prove that with high probability the size of both the max cut and maximum bisection are n 4 p 4 o o n n 4 p 4 o o n while the size of the minimum bisection is n 4 p 4 o o n n 4 p 4 o o n our derivation relates the free energy of the anti ferromagnetic ising model on such graphs to that of the sherrington kirkpatrick model with p 0 7632p 0 7632 standing for the ground state energy of the latter expressed analytically via parisi s formula

optimal cost sharing for resource selection games joint use of resources with usage dependent cost raises the question who pays how much we study cost sharing in resource selection games where the strategy spaces are either singletons or bases of a matroid defined on the ground set of resources our goal is to design cost sharing protocols so as to minimize the resulting price of anarchy and price of stability we investigate three classes of protocols basic protocols guarantee the existence of at least one pure nash equilibrium separable protocols additionally require that the resulting cost shares only depend on the set of players on a resource uniform protocols are separable and require that the cost shares on a resource may not depend on the instance that is they remain the same even if new resources are added to or removed from the instance we find optimal basic and separable protocols that guarantee the price of stability and price of anarchy to grow logarithmically in the number of players except for the case of matroid games induced by separable protocols where the price of anarchy grows linearly with the number of players for uniform protocols we show that the price of anarchy is unbounded even for singleton games

some effects of ignoring correlated measurement errors in straight line regression and prediction instructive expressions are developed for expected values of the least squares regression coefficient sample residual mean squared error and squared sample correlation coefficient in terms of a general measurement error model allowing for correlated measurement errors these expressions are useful in assessing the importance of measurement error in given applications and can be inverted to give simple estimators of measurement error model parameters based on the usual least squares estimates they show that in certain circumstances the correlation of variables contaminated with measurement errors can be greater than that of the uncontaminated variables these simple expressions should be useful in promoting the use of measurement error models in applications an example demonstrates that even in some cases where the least squares regression coefficient is affected little by measurement error valid estimation of the standard error of prediction may require the use of a measurement error model

estimation of relative potency with sequential dilution errors in radioimmunoassay summary sequential dilution is a very common procedure in radioimmunoassay in which the dilution error will be accumulated from the highest to the lowest concentration a simulated example in relative potency determination is used to demonstrate the potentially wrong conclusion that can be drawn when the dilution error is not properly included in the model a bayesian method is used and an alternative approximation via maximum likelihood is proposed an alternative experimental design is recommended to increase the precision of the inference

unipotent representations of complex semisimple groups algebraic group over r or c in this paper we restrict attention to c we generalize arthur s definition slightly or perhaps simply make it more precise all of the resulting representations except for a finite set are then unitarily induced from representations of the same kind on proper parabolic subgroups we call the finite set remaining special unipotent representations a precise definition will be given later definition 1 17 our main result theorem iii of this introduction is a character formula for any special unipotent representation of course such a formula can be deduced from the kazhdan lusztig conjecture cf v3 the advantages of theorem iii are that it is in closed form and that it lends itself to verification of some conjectures of arthur in a so let g be a connected complex semisimple lie group and q its lie algebra choose

cohomologically induced distinguished representations and cohomological test vectors let g be a real reductive group and let be a character of a reductive subgroup h of g we construct invariant linear functionals on certain cohomologically induced representations of g and we show that these linear functionals do not vanish on the bottom layers applying this construction we prove two archimedean nonvanishing hypotheses which are vital to the arithmetic study of special values of certain l functions via modular symbols

the multiplicities of certain k types in spherical representations abstract let g be a connected semisimple lie group with finite center g 0 its lie algebra g 0 k 0 p 0 a cartan decomposition of g 0 and let k be the corresponding maximal compact subgroup we denote the complexification of p 0 by p for an irreducible spherical representation x of g we compute dim hom k p x the result is given explicitly in terms of the langlands parameters of x

archimedean non vanishing cohomological test vectors and standard l functions of gl2n complex case abstract the purpose of this paper is to study the local zeta integrals of friedberg jacquet at complex place and to establish similar results to the recent work 4 joint with c chen and d jiang in this paper we will 1 give a necessary and sufficient condition on an irreducible essentially tempered cohomological representation of gl 2 n c with a non zero shalika model 2 construct a new twisted linear period s and give a different expression of the linear model for 3 give a necessary and sufficient condition on the character such that there exists a uniform cohomological test vector v v which we construct explicitly for s as a consequence we obtain the non vanishing of local friedberg jacquet integral at complex place all of the above are essential preparations for attacking a global period relation problem in the forthcoming paper 11

on the impact of combinatorial structure on congestion games we study the impact of combinatorial structure in congestion games on the complexity of computing pure nash equilibria and the convergence time of best response sequences in particular we investigate which properties of the strategy spaces of individual players ensure a polynomial convergence time we show that if the strategy space of each player consists of the bases of a matroid over the set of resources then the lengths of all best response sequences are polynomially bounded in the number of players and resources we also prove that this result is tight that is the matroid property is a necessary and sufficient condition on the players strategy spaces for guaranteeing polynomial time convergence to a nash equilibrium in addition we present an approach that enables us to devise hardness proofs for various kinds of combinatorial games including first results about the hardness of market sharing games and congestion games for overlay network design our approach also yields a short proof for the pls completeness of network congestion games in particular we show that network congestion games are pls complete for directed and undirected networks even in case of linear latency functions

on estimating linear relationships when both variables are subject to errors this paper discusses the problem of estimating a linear relationship between two variables observed with errors it focuses on confidence intervals for the slope parameter and confidence regions for the intercept and slope parameters in gaussian models a compendium of existing results as well as new results are presented

l packets of quasisplit gsp 2n and go 2n in his monograph arthur the endoscopic classification of representations orthogonal and symplectic groups colloquium publications american mathematical society providence 2013 characterizes the l packets of quasisplit symplectic groups and orthogonal groups by extending his work we characterize the l packets for the corresponding similitude groups with desired properties in particular we show these packets satisfy the conjectural endoscopic character identities

the hodge conjecture and arithmetic quotients of complex balls let s be a closed shimura variety uniformized by the complex n ball associated with a standard unitary group the hodge conjecture predicts that every hodge class in h 2k s mathbb q k 0 dots n is algebraic we show that this holds for all degrees k away from the neighborhood bigl tfrac13n tfrac23n bigr of the middle degree we also prove the tate conjecture for the same degrees as the hodge conjecture and the generalized form of the hodge conjecture in degrees away from an interval depending on the codimension c of the subvariety centered at the middle dimension of s these results are derived from a general theorem that applies to all shimura varieties associated with standard unitary groups of any signature the proofs make use of arthur s endoscopic classification of automorphic representations of classical groups as such our results rely on the stabilization of the trace formula for the disconnected groups gl n rtimes langle theta rangle associated with base change

computing pure nash and strong equilibria in bottleneck congestion games bottleneck congestion games properly model the properties of many real world network routing applications they are known to possess strong equilibria a strengthening of nash equilibrium to resilience against coalitional deviations in this paper we study the computational complexity of pure nash and strong equilibria in these games we provide a generic centralized algorithm to compute strong equilibria which has polynomial running time for many interesting classes of games such as e g matroid or single commodity bottleneck congestion games in addition we examine the more demanding goal to reach equilibria in polynomial time using natural improvement dynamics using unilateral improvement dynamics in matroid games pure nash equilibria can be reached efficiently in contrast computing even a single coalitional improvement move in matroid and single commodity games is strongly np hard in addition we establish a variety of hardness results and lower bounds regarding the duration of unilateral and coalitional improvement dynamics they continue to hold even for convergence to approximate equilibria

symmetric differentials kahler groups and ball quotients while margulis superrigidity theorem completely describes the finite dimensional linear representations of lattices of higher rank simple real lie groups almost nothing is known concerning the representation theory of complex hyperbolic lattices the main result of this paper theorem 1 3 is a strong rigidity theorem for a certain class of cocompact arithmetic complex hyperbolic lattices it relies on the following two ingredients theorem 1 6 showing that the representations of the topological fundamental group of a compact kahler manifold x are controlled by the global symmetric differentials on x an arithmetic vanishing theorem for global symmetric differentials on certain compact ball quotients using automorphic forms in particular deep results of clozel on base change theorem 1 11

duality between gl n r gl n qp and the degenerate affine hecke algebra for gl n we define an exact functor f n k from the category of harish chandra modules for rm gl n bbb r to the category of finite dimensional representations for the degenerate affine hecke algebra for frak g frak l k under certain natural hypotheses we prove that the functor maps standard modules to standard modules or zero and irreducibles to irreducibles or zero

a notion of rank for unitary representations of general linear groups a notion of rank for unitary representations of general linear groups over a locally compact nondiscrete field is defined rank measures how singular a representation is when restricted to the unipotent radical of a maximal parabolic subgroup irreducible representations of small rank are classified it is shown how rank determines to a large extent the asymptotic behavior of matrix coefficients of the representations i definition and basic properties of rank 0 introduction the unitary dual of gln f f a locally compact nondiscrete field has been classified by d vogan v in the archimedean case and up to the construction of all cuspidal representations by m tadic in the non archimedean case much remains to be done however in terms of the study of specific properties of the unitary representations involved the inspiration for this paper comes form the following well known theorem of howe and moore theorem 0 1 hm let g be a zariski connected reductive algebraic group over a nondiscrete locally compact field f and let p be a unitary representation of dimension greater than 1 such that the center z of g acts by a character then the absolute values of the matrix coefficients of p approach zero at infinity on g z an easy consequence of this is corollary 0 2 in the hypotheses for theorem 0 1 if n is a subgroup of g which is not compact modulo z any vector that is invariant under n transforms according to a character of g o in particular if p is irreducible and has a nontrivial n invariant vector p must be a character received by the editors august 15 1988 1980 mathematics subject classification 1985 revisiont primary 22e46 22e50 this paper was submitted in a different form in partial fulfillment of the requirements for doctor of philosophy in the department of mathematics of yale university the author acknowledges support from the consiglio nazionale delle ricerche italy 1990 american mathematical society 0002 9947 90 1 00 25 per page

potential automorphy and change of weight we prove an automorphy lifting theorem for l adic representations where we impose a new condition at l which we call potentential diagonalizability this result allows for change of weight and seems to be substantially more exible than previous theorems along the same lines we derive several applications for instance we show that any irreducible totally odd essentially self dual regular weakly compatible system of l adic representations of the absolute galois group of a totally real eld is potentially automorphic and hence is pure and its l function has meromorphic continuation to the whole complex plane and satises the expected functional equation

archimedean non vanishing cohomological test vectors and standard l functions of mathrm gl _ 2n gl2n real case the standard l functions of mathrm gl 2n expressed in terms of the friedberg jacquet global zeta integrals have better structure for arithmetic applications due to the relation of the linear periods with the modular symbols the most technical obstacles towards such arithmetic applications are 1 non vanishing of modular symbols at infinity and 2 the existence or construction of uniform cohomological test vectors problem 1 is also called the non vanishing hypothesis at infinity which was proved by sun duke math j 168 1 85 126 2019 theorem 5 1 by establishing the existence of certain cohomological test vectors in this paper we explicitly construct an archimedean local integral that produces a new type of a twisted linear functional lambda s chi which when evaluated with our explicitly constructed cohomological vector is equal to the local twisted standard l function l s pi otimes chi for all complex values s with the relations between linear models and shalika models we establish 1 with an explicitly constructed cohomological vector using classical invariant theory and hence proves the non vanishing results of sun 24 theorem 5 1 via a completely different method

local approximation of the maximum cut in regular graphs abstract this paper is devoted to the distributed complexity of finding an approximation of the maximum cut maxcut in graphs a classical algorithm consists in letting each vertex choose its side of the cut uniformly at random this does not require any communication and achieves an approximation ratio of at least 1 2 in expectation when the graph is d regular and triangle free a slightly better approximation ratio can be achieved with a randomized algorithm running in a single round here we investigate the round complexity of deterministic distributed algorithms for maxcut in regular graphs we first prove that if g is d regular with d even and fixed no deterministic algorithm running in a constant number of rounds can achieve a constant approximation ratio we then give a simple one round deterministic algorithm achieving an approximation ratio of 1 d for d regular graphs when d is odd we show that this is best possible in several ways and in particular no deterministic algorithm with approximation ratio 1 d with 0 can run in a constant number of rounds we also prove results of a similar flavor for the maxdicut problem in regular oriented graphs where we want to maximize the number of arcs oriented from the left part to the right part of the cut

likelihood analysis for errors in variables regression with replicate measurements summary this paper advocates likelihood analysis for regression models with measurement errors in explanatory variables for data problems in which the relevant distributions can be adequately modelled although computationally difficult maximum likelihood estimates are more efficient than those based on first and second moment assumptions and likelihood ratio inferences can be substantially better than those based on asymptotic normality of estimates the em algorithm is presented as a straightforward approach for likelihood analysis of normal linear regression with normal explanatory variables and normal replicate measurements likelihood methods for regression analysis with explanatory variable measurement error have received little attention relative to methods based on first and second moment assumptions largely because of computational difficulties uncertainty about the robustness of likelihood methods and the belief that the simpler methods perform just as well in practice with improved computational tools for likelihood analysis as discussed for example by tanner 1993 it is worthwhile to reinvestigate these issues in particular the common belief that the simpler methods perform just as well as likelihood methods may be naive first the comparison is usually cast in terms of efficiency without regard to test and confidence interval validity likelihood ratio tests and confidence intervals can be substantially better than tests and confidence intervals based on estimates and standard errors of the commonly used method of moments approaches the sampling distributions of the estimators are very often skewed especially if the measurement errors are large furthermore knowledge about the relative efficiency of the moment methods comes from a small number of efficiency comparisons from simulations of isolated situations in papers promoting these simpler methods carroll rupert stefanski 1995 7 1 an important and often overlooked issue is that the moment methods may be especially inappropriate when the distribution of the true covariates is skewed pierce et al 1992 section 2 discusses computational approaches and difficulties associated with likelihood analysis in the measurement error problem generally section 3 illustrates the em algorithm dempster laird rubin 1977 for likelihood analysis of normal linear regression with a normally distributed explanatory variable measured with normally distributed error when there are replicate measurements for at least some of the cases sections 5 and 6

lower bounds for local approximation in the study of deterministic distributed algorithms it is commonly assumed that each node has a unique o log n bit identifier we prove that for a general class of graph problems local algorithms constant time distributed algorithms do not need such identifiers a port numbering and orientation is sufficient our result holds for so called simple po checkable graph optimisation problems this includes many classical packing and covering problems such as vertex covers edge covers matchings independent sets dominating sets and edge dominating sets we focus on the case of bounded degree graphs and show that if a local algorithm finds a constant factor approximation of a simple po checkable graph problem with the help of unique identifiers then the same approximation ratio can be achieved on anonymous networks as a corollary of our result we derive a tight lower bound on the local approximability of the minimum edge dominating set problem by prior work there is a deterministic local algorithm that achieves the approximation factor of 4 1 2 in graphs of maximum degree this approximation ratio is known to be optimal in the port numbering model our main theorem implies that it is optimal also in the standard model in which each node has a unique identifier our main technical tool is an algebraic construction of homogeneously ordered graphs we say that a graph is r homogeneous if its nodes are linearly ordered so that an fraction of nodes have pairwise isomorphic radius r neighbourhoods we show that there exists a finite r homogeneous 2k regular graph of girth at least g for any

generalized least squares with ignored errors in variables we present data both real and simulated that show generalized least squares gls estimation intended to account for correlated response error structure can produce gross biasing in regression parameter estimates under misspecified models with ignored errors in explanatory variable measurements the bias and its subsequent effect on mean squared error mse can be much more severe than the apparently less appropriate ordinary least squares ols estimator this article provides a theoretical basis for these effects by deriving expressions for the bias and mse for the general gls estimator through taylor series expansions the results are compared with simulations for two specific weight matrices and applied to a dataset relating atmospheric pollutant levels in los angeles with average recorded wind speed we show that the bias with subsequent implications for the mse is always worse for the exponential correlation model with equally spaced explanatory variable observations and present a simple tes

kazhdan lusztig algorithms for nonlinear groups and applications to kazhdan patterson lifting we establish an algorithm to compute characters of irreducible harish chandra modules for a large class of nonalgebraic lie groups roughly speaking the class of groups consists of those obtained as nonlinear double covers of linear groups in harish chandra s class we then apply this theory to study a particular group the universal cover of the real general linear group and discover a symmetry of the character computations encoded in a character multiplicity duality using this duality theory we reinterpret a kind of representation theoretic shimura correspondence for the general linear group geometrically and find that it is dual to an analogous lifting for indefinite unitary groups it seems likely that this example is illustrative of a general framework for studying similar correspondences

degenerate principal series representations of gln c and gln r let f be the field c or r for 1 k n 2 let pk be the maximal parabolic subgroup of gln f with its levi factor isomorphic to gln k f glk f in this paper we explicitly calculate the action of the enveloping algebra of gln f on the degenerate principal series representations induced from characters of pk we address composition series k types and unitarity