Dmodules and automorphic induction

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August undefined, 2024

WebMay 1, 2010 · That gives a process of “automorphic induction” which to an irreducible (g,K)- module τ for GL(n,C) associates an irreducible (g,K)-module π = τ C/R for GL(2n,R). In the present paper we show that if τ is unitary and generic then π is determined by τ, up to isomorphism, via a character identity entirely analogous to the character ... WebNov 1, 2024 · Using Langlands functoriality and automorphic induction, it gives an automorphic cuspidal representation of GL 2 (A Q). The relation between the automorphic representations of GL 2 (A Q) and the cuspidal cohomology of GL 2 can be described in terms of the sheaf M ˜ μ associated to the highest weight representation M μ of GL (2, …

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http://faculty.bicmr.pku.edu.cn/~lxiao/2024spring/Notes9-Lu.pdf Web11F52 Modular forms associated to Drinfeld modules; 11F55 Other groups and their modular and automorphic forms (several variables) 11F60 Hecke-Petersson operators, ... Lafforgue has proposed a new approach to the principle of functoriality in a test case, namely, the case of automorphic induction from an idele class character of a quadratic ... christine margarete anderson

Induction automorphe pour GL(n,C) - ResearchGate

Webfor the automorphic induction exists for generic cuspidal automorphic representations. By using this automorphic induction, we give a con-jectural criterion on the existence of poles of L(s;ˇ;^3 ˜) for discrete automorphic representations in the tempered spectrum. Contents 1. Introduction2 2. Integral representation5 2.1. Global zeta ... WebVarieties of modules of F-sheaves. V. G. Drinfel'd. Functional Analysis and Its Applications 21 , 107–122 ( 1987) Cite this article. 420 Accesses. 41 Citations. WebMonoidal Structures on GLp2q-Modules and Abstractly Automorphic Representations Gal Dor Tel-Aviv University March 04, 2024 1/24. Introduction p-adic reps GJ vs. JL Monoidal structure Apology Global theory ... Compact induction of SpM 2pFqqfrom GL 2pFq3;det 1 to GL 2pFq3 gives Y. 11/24. christine marchand acupression

Period Relations and Special Values of Rankin-Selberg

An example of non-normal quintic automorphic induction and …

WebAug 6, 2024 · This procedure should conjecturally realize the automorphic induction from T to G. For G = GL_2, we prove that our construction indeed realizes the automorphic induction from at most tamely ... WebFeb 1, 2015 · Let K be a quadratic imaginary field. Let Π (resp. Π ′) be a regular algebraic cuspidal representation of GL n (A K) (resp. GL n − 1 (A K)), which is moreover … christine margaret andersonWebfor the automorphic induction exists for generic cuspidal automorphic representations. By using this automorphic induction, we give a con-jectural criterion on the existence of … christine margaret o\u0027shea

"Webdrawback. This article contributes to the automorphic induction over local elds by introducing a new construction of type (ii), which works for all tori and all reductive groups (in the equal characteristic case). orF G GL 2 we prove that our construction indeed realizes the ‘-adic automorphic induction for all at most tamely rami ed tori. " - Dmodules and automorphic induction

Dmodules and automorphic induction

Introduction to automorphic representations (DRAFT!)

WebIntroductory lectures on automorphic forms Lectures for the European School of Group Theory July, 2001, Luminy, France by Nolan R. Wallach 1 Orbital integrals and the … WebLet K be a quadratic imaginary field. Let Π (resp. Π1) be a regular algebraic cuspidal representation of GLnpAKq (resp. GLn ́1pAKq) which is moreover cohomological and conjugate self-dual. When Π is a cyclic automorphic induction of a Hecke character χ over a CM field, we show relations between automorphic periods of Π defined by Harris and …

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WebApr 1, 2006 · The basics of the theory of Hilbert Q-modules are established. Using this approach to V-semilattices with a duality i.e. Hilbert 2-modules, we describe a nuclear traced ideal and characterize ... WebMay 1, 2024 · Automorphic induction of class group characters. Let K / Q be a degree n extension. Let χ be a non-trivial Hecke character of K, and let I K Q χ be the automorphic induction. Since χ is non-trivial, L (s, χ) = L (s, I K Q χ) is entire. However, the automorphy of I K Q χ is proved only in certain cases, namely, it is an automorphic ...

WebProof. Recall that A 1 ·A 1 ⊂A 2.By almost commutativity for all a,b∈A 1, ab= bamodA 1.Therefore (ab−ba) ∈A 1 and A 1 acquires the structure of a Lie algebra. By the …

WebOct 20, 2014 · 27.5.3 Harish-Chandra modules. 27.6 Representations of l-groups: the Hecke algebra. 28 Automorphic forms and the Hecke algebra. 28.1 The case of SL 2 – … WebDrinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications is based on the author’s original work establishing the correspondence between ell-adic rank r Galois …

WebIt is conjectured that an automorphic representation of GL n associated to K induces an automorphic representation of GL r n associated to F. The book by Arthur and Clozel …

WebLet K be a quadratic imaginary field. Let Π (resp. Π1) be a regular algebraic cuspidal representation of GLnpAKq (resp. GLn ́1pAKq) which is moreover cohomological and … german breed of sheepWebalgebra for GLn over CM ﬁelds without needing to assume automorphic induction of characters for the extension K/Q. For this methods of potential automorphy results are used. Contents. 1. Introduction. 1.1. Notation. 2. Preliminaries in commutative algebra. 2.1. Change of coefﬁcients. 2.2. Minimal complexes and the derived category. 2.3 ... german breeding campsWeb6. Twisted Automorphic Descents 57 6.1. Automorphic descents and certain Arthur packets 57 6.2. Construction of cuspidal automorphic modules 66 6.3. Global Gan-Gross-Prasad conjecture: another direction 69 7. On the Main Conjecture 73 7.1. The main conjecture: general case 73 7.2. The main conjecture: regular orbit case 75 7.3. german breed of dog with webbed feetWebQuintic automorphic induction 497 respect to a congruence subgroup of SL 2(Z); Deligne-Serre Theorem [D-S] implies that π gives rise to an odd irreducible 2-dimensional representation of the Galois group ρ: GQ−→ GL 2(C).The converse is a special case of a strong Artin conjecture, namely, given an odd irreducible representation christine margaret yorathWebDRINFELD MODULI SCHEMES AND AUTOMORPHIC FORMS 3 Introduction Let F be a geometric global eld, of characteristic p>0, A its ring of ad eles, G= GL(r) and ˇan … german brewery beer glass collectionsWebThe Hodge-Tate period map is an important, new tool for studying the geometry of Shimura varieties, p-adic automorphic forms and torsion classes in the cohomology of Shimura varieties. It is a G (A_f)-equivariant map from a perfectoid Shimura variety into a flag variety with only an action of G (Q_p) and can be thought of as a p-adic analogue ... christine margaret storeyWebDrinfeld modules. G. W. Anderson [1] saw correctly how to develop the theory of higher dimensional Drinfeld modules, called t-modules, and at the same time produced a … german brewery creates powdered beer