scholarly journals Local intertwining relation for metaplectic groups

2020 ◽  
Vol 156 (8) ◽  
pp. 1560-1594
Author(s):  
Hiroshi Ishimoto
Keyword(s):  
Local Field ◽  
Characteristic Zero ◽  
Orthogonal Groups ◽  
Metaplectic Groups ◽  
Langlands Correspondence ◽  
Intertwining Relation ◽  
Local Langlands Correspondence

AbstractIn an earlier paper of Wee Teck Gan and Gordan Savin, the local Langlands correspondence for metaplectic groups over a nonarchimedean local field of characteristic zero was established. In this paper, we formulate and prove a local intertwining relation for metaplectic groups assuming the local intertwining relation for non-quasi-split odd special orthogonal groups.

scholarly journals Endo-parameters for p-adic classical groups

2020 ◽  
Author(s):  
Robert Kurinczuk ◽  
Daniel Skodlerack ◽  
Shaun Stevens
Keyword(s):  
Local Field ◽  
Classical Group ◽  
Linear Groups ◽  
Closed Field ◽  
Classical Groups ◽  
Langlands Correspondence ◽  
General Linear Groups ◽  
Langlands Parameters ◽  
Local Langlands Correspondence ◽  
Residual Characteristic

Abstract For a classical group over a non-archimedean local field of odd residual characteristic p, we prove that two cuspidal types, defined over an algebraically closed field $${\mathbf {C}}$$ C of characteristic different from p, intertwine if and only if they are conjugate. This completes work of the first and third authors who showed that every irreducible cuspidal $${\mathbf {C}}$$ C -representation of a classical group is compactly induced from a cuspidal type. We generalize Bushnell and Henniart’s notion of endo-equivalence to semisimple characters of general linear groups and to self-dual semisimple characters of classical groups, and introduce (self-dual) endo-parameters. We prove that these parametrize intertwining classes of (self-dual) semisimple characters and conjecture that they are in bijection with wild Langlands parameters, compatibly with the local Langlands correspondence.

scholarly journals THE -MODULAR LOCAL LANGLANDS CORRESPONDENCE AND LOCAL CONSTANTS

2019 ◽  
pp. 1-51 ◽  
Author(s):  
R. Kurinczuk ◽  
N. Matringe
Keyword(s):  
Prime Number ◽  
Local Field ◽  
Equivalence Classes ◽  
Modular Representations ◽  
Langlands Correspondence ◽  
Weil Group ◽  
Local Langlands Correspondence ◽  
Residual Characteristic

Let  $F$ be a non-archimedean local field of residual characteristic  $p$ , $\ell \neq p$ be a prime number, and  $\text{W}_{F}$ the Weil group of  $F$ . We classify equivalence classes of  $\text{W}_{F}$ -semisimple Deligne  $\ell$ -modular representations of  $\text{W}_{F}$ in terms of irreducible  $\ell$ -modular representations of  $\text{W}_{F}$ , and extend constructions of Artin–Deligne local constants to this setting. Finally, we define a variant of the  $\ell$ -modular local Langlands correspondence which satisfies a preservation of local constants statement for pairs of generic representations.

scholarly journals Representations of metaplectic groups I: epsilon dichotomy and local Langlands correspondence

2012 ◽  
Vol 148 (6) ◽  
pp. 1655-1694 ◽  
Author(s):  
Wee Teck Gan ◽  
Gordan Savin
Keyword(s):  
Irreducible Representations ◽  
Metaplectic Groups ◽  
Theta Correspondence ◽  
Langlands Correspondence ◽  
Local Langlands Correspondence ◽  
Shimura Correspondence

AbstractUsing theta correspondence, we classify the irreducible representations of Mp2n in terms of the irreducible representations of SO2n+1 and determine many properties of this classification. This is a local Shimura correspondence which extends the well-known results of Waldspurger for n=1.

scholarly journals Transfert d’intégrales orbitales pour le groupe métaplectique

2010 ◽  
Vol 147 (2) ◽  
pp. 524-590 ◽  
Author(s):  
Wen-Wei Li
Keyword(s):  
Trace Formula ◽  
Local Field ◽  
Transfer Factor ◽  
Characteristic Zero ◽  
Prior Work ◽  
Selberg Trace Formula ◽  
Metaplectic Groups ◽  
Orbital Integrals ◽  
Fundamental Lemma ◽  
Set Up

AbstractWe set up a formalism of endoscopy for metaplectic groups. By defining a suitable transfer factor, we prove an analogue of the Langlands–Shelstad transfer conjecture for orbital integrals over any local field of characteristic zero, as well as the fundamental lemma for units of the Hecke algebra in the unramified case. This generalizes prior work of Adams and Renard in the real case and serves as a first step in studying the Arthur–Selberg trace formula for metaplectic groups.

scholarly journals SPECTRAL TRANSFER FOR METAPLECTIC GROUPS. I. LOCAL CHARACTER RELATIONS

2016 ◽  
Vol 18 (1) ◽  
pp. 25-123 ◽  
Author(s):  
Wen-Wei Li
Keyword(s):  
Internal Structure ◽  
Local Field ◽  
Characteristic Zero ◽  
Test Functions ◽  
Metaplectic Groups ◽  
Transfer Factors ◽  
Orbital Integrals ◽  
The Core ◽  
Local Character ◽  
Stable Trace Formula

Let $\widetilde{\text{Sp}}(2n)$ be the metaplectic covering of $\text{Sp}(2n)$ over a local field of characteristic zero. The core of the theory of endoscopy for $\widetilde{\text{Sp}}(2n)$ is the geometric transfer of orbital integrals to its elliptic endoscopic groups. The dual of this map, called the spectral transfer, is expected to yield endoscopic character relations which should reveal the internal structure of $L$-packets. As a first step, we characterize the image of the collective geometric transfer in the non-archimedean case, then reduce the spectral transfer to the case of cuspidal test functions by using a simple stable trace formula. In the archimedean case, we establish the character relations and determine the spectral transfer factors by rephrasing the works by Adams and Renard.

scholarly journals On the Notion of Conductor in the Local Geometric Langlands Correspondence

2017 ◽  
Vol 69 (1) ◽  
pp. 107-129
Author(s):  
Masoud Kamgarpour
Keyword(s):  
Irreducible Representation ◽  
Galois Representation ◽  
Loop Group ◽  
Langlands Correspondence ◽  
Categorical Representation ◽  
Swan Conductor ◽  
Geometric Langlands ◽  
Meromorphic Connection ◽  
Local Langlands Correspondence ◽  
Geometric Analogue

AbstractUnder the local Langlands correspondence, the conductor of an irreducible representation of Gln(F) is greater than the Swan conductor of the corresponding Galois representation. In this paper, we establish the geometric analogue of this statement by showing that the conductor of a categorical representation of the loop group is greater than the irregularity of the corresponding meromorphic connection.

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