On Some Early Sources for the Notion of Transfer in Langlands Functoriality: Part I An Overview with Examples

2021 ◽  
pp. 387-400
Author(s):  
Diana Shelstad
Keyword(s):  
Langlands Functoriality

scholarly journals Models of Representations and Langlands Functoriality

2019 ◽  
Vol 72 (3) ◽  
pp. 676-707 ◽  
Author(s):  
Arnab Mitra ◽  
Eitan Sayag
Keyword(s):  
Base Change ◽  
General Linear ◽  
Linear Groups ◽  
General Linear Groups ◽  
Whittaker Model ◽  
Automorphic Induction ◽  
Ladder Representations ◽  
Langlands Functoriality ◽  
Whittaker Models

AbstractIn this article we explore the interplay between two generalizations of the Whittaker model, namely the Klyachko models and the degenerate Whittaker models, and two functorial constructions, namely base change and automorphic induction, for the class of unitarizable and ladder representations of the general linear groups.

scholarly journals Geometric Weil representation: local field case

2009 ◽  
Vol 145 (1) ◽  
pp. 56-88 ◽  
Author(s):  
Vincent Lafforgue ◽  
Sergey Lysenko
Keyword(s):  
Local Field ◽  
Dual Pair ◽  
Weil Representation ◽  
Closed Field ◽  
Perverse Sheaves ◽  
Algebraically Closed Field ◽  
Field Case ◽  
Metaplectic Group ◽  
Geometric Langlands ◽  
Langlands Functoriality

AbstractLet k be an algebraically closed field of characteristic greater than 2, and let F=k((t)) and G=𝕊p2d. In this paper we propose a geometric analog of the Weil representation of the metaplectic group $\widetilde G(F)$. This is a category of certain perverse sheaves on some stack, on which $\widetilde G(F)$ acts by functors. This construction will be used by Lysenko (in [Geometric theta-lifting for the dual pair S𝕆2m, 𝕊p2n, math.RT/0701170] and subsequent publications) for the proof of the geometric Langlands functoriality for some dual reductive pairs.

On Local L-Functions and Normalized Intertwining Operators

2005 ◽  
Vol 57 (3) ◽  
pp. 535-597 ◽  
Author(s):  
Henry H. Kim
Keyword(s):  
Eisenstein Series ◽  
Constant Term ◽  
Intertwining Operators ◽  
Local Results ◽  
Langlands Functoriality

AbstractIn this paper we make explicit all L-functions in the Langlands–Shahidi method which appear as normalizing factors of global intertwining operators in the constant term of the Eisenstein series. We prove, in many cases, the conjecture of Shahidi regarding the holomorphy of the local L-functions. We also prove that the normalized local intertwining operators are holomorphic and non-vaninishing for Re(s) ≥ 1/2 in many cases. These local results are essential in global applications such as Langlands functoriality, residual spectrumand determining poles of automorphic L-functions.

scholarly journals Langlands Functoriality Conjecture

2009 ◽  
Vol 49 (2) ◽  
pp. 355-387
Author(s):  
Jae-Hyun Yang
Keyword(s):  
Langlands Functoriality

scholarly journals Level-raising and symmetric power functoriality, I

2014 ◽  
Vol 150 (5) ◽  
pp. 729-748 ◽  
Author(s):  
Laurent Clozel ◽  
Jack A. Thorne
Keyword(s):  
Tensor Product ◽  
Recent Result ◽  
Number Field ◽  
Deformation Theory ◽  
Automorphic Representation ◽  
Symmetric Power ◽  
Classical Type ◽  
Initial Representation ◽  
Totally Real ◽  
Langlands Functoriality

AbstractAs the simplest case of Langlands functoriality, one expects the existence of the symmetric power $S^n(\pi )$, where $\pi $ is an automorphic representation of ${\rm GL}(2,{\mathbb{A}})$ and ${\mathbb{A}}$ denotes the adeles of a number field $F$. This should be an automorphic representation of ${\rm GL}(N,{\mathbb{A}})$ ($N=n+1)$. This is known for $n=2,3$ and $4$. In this paper we show how to deduce the general case from a recent result of J.T. on deformation theory for ‘Schur representations’, combined with expected results on level-raising, as well as another case (a particular tensor product) of Langlands functoriality. Our methods assume $F$ totally real, and the initial representation $\pi $ of classical type.

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