on the standard modules conjecture let g be a quasi split p adic group under the assumption that the local coefficients c defined with respect to generic tempered representations of standard levi subgroups of g are regular in the negative weyl chamber we show that the standard module conjecture is true which means that the langlands quotient of a standard module is generic if and only if the standard module is irreducible

une preuve simple des conjectures de langlands pour gl n sur un corps p adique let f be a finite extension of p for each integer n 1 we construct a bijection from the set f 0 n of isomorphism classes of irreducible degree n representations of the absolute weil group of f onto the set f 0 n of isomorphism classes of smooth irreducible supercuspidal representations of gl n f those bijections preserve epsilon factors for pairs and hence we obtain a proof of the langlands conjectures for gl n over f which is more direct than harris and taylor s our approach is global and analogous to the derivation of local class field theory from global class field theory we start with a result of kottwitz and clozel on the good reduction of some shimura varieties and we use a trick of harris who constructs non galois automorphic induction in certain cases

a theory of miyawaki liftings the hilbert siegel case the miyawaki liftings are defined by the pullbacks of ikeda liftings recently ikeda and yamana extended the theory of ikeda liftings to hilbert siegel modular forms in this paper using their results we establish a theory of miyawaki liftings both locally and globally in the local theory we describe the miyawaki liftings for almost tempered unitary representations explicitly in the global theory we discuss the non vanishing of the miyawaki liftings using seesaw identities and the global gan gross prasad conjecture as an application of local miyawaki liftings we prove a new case of the local gan gross prasad conjecture

jacquet modules and local langlands correspondence in this paper we explicitly compute the semisimplifications of all jacquet modules of irreducible representations with generic l parameters of p adic split odd special orthogonal groups or symplectic groups our computation represents them in terms of linear combinations of standard modules with rational coefficients the main ingredient of this computation is to apply m glin s explicit construction of local a packets to tempered l packets finally we study the derivatives introduced by minguez

multiplicity one theorems for fourier jacobi models for every genuine irreducible admissible smooth representation pi of the metaplectic group widetilde rm sp 2n over a p adic field and every smooth oscillator representation omega psi of widetilde rm sp 2n we prove that the tensor product pi otimes omega psi is multiplicity free as a smooth representation of the symplectic group rm sp 2n similar results are proved for general linear groups and unitary groups

the regularized siegel weil formula the second term identity and the rallis inner product formula in this paper we establish the second term identity of the siegel weil formula in full generality and derive the rallis inner product formula for global theta lifts for any dual pair as a corollary we resolve the non vanishing problem of global theta lifts initiated by steve rallis

percentage points for a generalized esd many outlier procedure a generalized extreme studentized deviate esd many outlier procedure is given for detecting from 1 to k outliers in a data set this procedure has an advantage over the original esd many outlier procedure rosner 1975 in that it controls the type i error both under the hypothesis of no outliers and under the alternative hypotheses of 1 2 k l outliers a method is given for approximating percentiles for this procedure based on the t distribution this method is shown to be adequately accurate using monte carlo simulation for detecting up to 10 outliers in samples as small as 25 tables are given for implementing this method for n 25 1 50 10 100 50 500 k 10 05 ol 005

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

a local trace formula for the generalized shalika model we study a local multiplicity problem related to so called generalized shalika models by establishing a local trace formula for these kinds of models we are able to prove a multiplicity formula for discrete series as a result we can show that these multiplicities are for discrete series invariant under the local jacquet langlands correspondence and are related to local exterior square l functions

local theta correspondence of tempered representations and langlands parameters in this paper we give an explicit determination of the theta lifting for symplectic orthogonal and unitary dual pairs over a nonarchimedean field f of characteristic 0 we determine when theta lifts of tempered representations are nonzero and determine the theta lifts in terms of the local langlands correspondence

the gross prasad conjecture and local theta correspondence we establish the fourier jacobi case of the local gross prasad conjecture for unitary groups by using local theta correspondence to relate the fourier jacobi case with the bessel case established by beuzart plessis to achieve this we prove two conjectures of prasad on the precise description of the local theta correspondence for almost equal rank unitary dual pairs in terms of the local langlands correspondence the proof uses arthur s multiplicity formula and thus is one of the first examples of a concrete application of this global reciprocity law

multiplicity one theorems in the local characteristic 0 non archimedean case we consider distributions on gl n 1 which are invariant under the adjoint action of gl n we prove that such distributions are invariant by transposition this implies multiplicity at most one for restrictions from gl n 1 to gl n similar theorems are obtained for orthogonal or unitary groups

theta lifts and distinction for regular supercuspidal representations this article has a twofold purpose first by recent works of kaletha and loke ma we give an explicit description of the local theta correspondence between regular supercuspidal representations in the equal rank symplectic orthogonal case second based on this description we show that the local theta correspondence preserves distinction with respect to unramified galois involutions

theta dichotomy for unitary groups some recent work of gross and prasad 14 suggests that the root numbers attached to certain symplectic representations of the weil deligne group of a local field f control certain branching rules for representations of orthogonal groups over f on a global level this local phenomenon should have implications for the structure of the value at the center of symmetry for certain l functions of arithmetic interest 12 this conjectural picture is based to some extent on the now classic work of tunnell 47 and waldspurger 49 as well as on the case of the triple product l function 13 34 17 in all of these examples the local root number detects the existence of a certain type of invariant linear functional it is possible to set up analogous conjectures for the isometry groups of hermitian or quaternion hermitian forms it turns out that root numbers also play a role in the local and global theta correspondence roughly speaking certain local root numbers should control the occurrence of representations in the local theta correspondence between groups of the same size e g for dual pairs of the form sp n o 2n 1 and u n u n as will be seen the theta correspondence for such pairs is connected with a certain induced representation in s at the point s 0 on the unitary axis by contrast the correspondence for the pairs sp n o 2n and sp n o 2n 2 discussed by prasad 35 is connected to the behavior of a similar induced representation at the points 12 in which case no epsilon factor arises in this paper we consider the local theta correspondence for unitary groups in the non archimedean case let f be a non archimedean local field of characteristic not equal to 2 and let e be a quadratic extension of f for further notation see the notation section at the end of this introduction let v and w be e vector spaces of dimensions m and n equipped respectively with a hermitian form v v e and a skew hermitian form w w e then the isometry groups g v and g w of the spaces v and w form a dual reductive pair in the symplectic group sp w where w v e w viewed as an f vector space of dimension 2mn and equipped with the symplectic form

the breakdown points of the mean combined with some rejection rules in the past methods for rejection of outliers have been investigated mostly without regard to the quantitative consequences for subsequent estimation or testing procedures moreover although rejection of outliers with subsequent application of least squares methods is one of the oldest and most widespread classes of robust procedures until recently no comparison was made with other robust methods in this article the simplest situation namely estimation of a location parameter in the potential presence of outliers is treated by means of a monte carlo study this study yields monte carlo variances of the arithmetic mean after rejection of outliers according to several classical and recent formal rules the results are also compared with those for other robust estimators of location parameters it turns out that a simple summary and theoretical explanation of the monte carlo results is provided by the breakdown points of the combined rejection estimation procedures as a by product the concept of br

the bee identification error exponent with absentee bees the bee identification problem was formally defined by tandon tan and varshney ieee trans commun vol 67 2019 and the error exponent was studied this work extends the results for the absentee bees scenario where a fraction of the bees are absent in the beehive image used for identification for this setting we present an exact characterization of the bee identification error exponent and show that independent barcode decoding is optimal i e joint decoding of the bee barcodes does not result in a better error exponent relative to independent decoding of each noisy barcode this is in contrast to the result without absentee bees where joint barcode decoding results in a significantly higher error exponent than independent barcode decoding we also define and characterize the capacity for the bee identification problem with absentee bees and prove a strong converse for the same

on the gan gross prasad problem for finite unitary groups in this paper we study the gan gross prasad problem for unitary groups over finite fields our results provide complete answers for unipotent representations and we obtain the explicit branching of these representations

the local langlands correspondence for gln over p adic fields we extend our methods from scholze invent math 2012 doi 10 1007 s00222 012 0419 y to reprove the local langlands correspondence for gl n over p adic fields as well as the existence of l adic galois representations attached to most regular algebraic conjugate self dual cuspidal automorphic representations for which we prove a local global compatibility statement as in the book of harris taylor the geometry and cohomology of some simple shimura varieties 2001 in contrast to the proofs of the local langlands correspondence given by henniart invent math 139 2 439 455 2000 and harris taylor the geometry and cohomology of some simple shimura varieties 2001 our proof completely by passes the numerical local langlands correspondence of henniart ann sci ec norm super 21 4 497 544 1988 instead we make use of a previous result from scholze invent math 2012 doi 10 1007 s00222 012 0419 y describing the inertia invariant nearby cycles in certain regular situations

on the non vanishing of theta liftings of tempered representations of u p q abstract in this paper we give an explicit determination of the non vanishing of the theta liftings of tempered representations for unitary dual pairs u p q u r s for arbitrary non negative integers p q r s for discrete series representations in terms of harish chandra parameters we give a complete criterion when the theta lifts are nonzero for tempered representations we determine the non vanishing in terms of the local langlands correspondence assuming the local gan gross prasad conjecture

the local theta correspondence and the local gan gross prasad conjecture for the symplectic metaplectic case we prove the local gan gross prasad conjecture for the symplectic metaplectic case under some assumptions this is the last case of the local gan gross prasad conjectures which has not been established we also prove two of prasad s conjectures on the local theta correspondence in the almost equal rank case

le lemme fondamental pondere ii enonces cohomologiques dans cet article on etudie la cohomologie de la fibration de hitchin tronquee introduite dans un article precedent on etend les principaux theoremes de ngo sur la cohomologie de la partie elliptique de la fibration de hitchin comme consequence on obtient une demonstration du lemme fondamental pondere d arthur in this paper we study the cohomology of the truncated hitchin fibration which was introduced in a previous paper we extend ngo s main theorems on the cohomology of the elliptic part of the hitchin fibration as a consequence we get a proof of arthur s weighted fundamental lemma

the identification of multiple outliers abstract one approach to identifying outliers is to assume that the outliers have a different distribution from the remaining observations in this article we define outliers in terms of their position relative to the model for the good observations the outlier identification problem is then the problem of identifying those observations that lie in a so called outlier region methods based on robust statistics and outward testing are shown to have the highest possible breakdown points in a sense derived from donoho and huber but a more detailed analysis shows that methods based on robust statistics perform better with respect to worst case behavior a concrete outlier identifier based on a suggestion of hampel is given