scholarly journals Local Langlands Correspondence for Regular Supercuspidal Representations of GL(n)

2020 ◽  
Author(s):  
Masao Oi ◽  
Kazuki Tokimoto
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
Langlands Correspondence ◽  
Supercuspidal Representations ◽  
General Linear Groups ◽  
The Difference ◽  
Local Langlands Correspondence

Abstract In this paper, we prove the coincidence of Kaletha’s recent construction of the local Langlands correspondence for regular supercuspidal representations with Harris–Taylor’s one in the case of general linear groups. The keys are Bushnell–Henniart’s essentially tame local Langlands correspondence and Tam’s result on Bushnell–Henniart’s rectifiers. By combining them, our problem is reduced to an elementary root-theoretic computation on the difference between Kaletha’s and Tam’s $\chi $-data.

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 Unitary dual of GL(n) at archimedean places and global Jacquet–Langlands correspondence

2010 ◽  
Vol 146 (5) ◽  
pp. 1115-1164 ◽  
Author(s):  
A. I. Badulescu ◽  
D. Renard
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
Automorphic Representations ◽  
Langlands Correspondence ◽  
General Linear Groups ◽  
Multiplicity One ◽  
Unitary Dual ◽  
Strong Multiplicity ◽  
Local Results

AbstractIn a paper by Badulescu [Global Jacquet–Langlands correspondence, multiplicity one and classification of automorphic representations, Invent. Math. 172 (2008), 383–438], results on the global Jacquet–Langlands correspondence, (weak and strong) multiplicity-one theorems and the classification of automorphic representations for inner forms of the general linear group over a number field were established, under the assumption that the local inner forms are split at archimedean places. In this paper, we extend the main local results of that article to archimedean places so that the above condition can be removed. Along the way, we collect several results about the unitary dual of general linear groups over ℝ, ℂ or ℍ which are of independent interest.

ON THE LOCAL LANGLANDS CORRESPONDENCE FOR SPLIT CLASSICAL GROUPS OVER LOCAL FUNCTION FIELDS

2015 ◽  
Vol 16 (5) ◽  
pp. 987-1074 ◽  
Author(s):  
Radhika Ganapathy ◽  
Sandeep Varma
Keyword(s):  
Representation Theory ◽  
Function Fields ◽  
Local Fields ◽  
Linear Groups ◽  
Classical Groups ◽  
Local Function ◽  
Langlands Correspondence ◽  
General Linear Groups ◽  
Residue Characteristic ◽  
Local Langlands Correspondence

We prove certain depth bounds for Arthur’s endoscopic transfer of representations from classical groups to the corresponding general linear groups over local fields of characteristic 0, with some restrictions on the residue characteristic. We then use these results and the method of Deligne and Kazhdan of studying representation theory over close local fields to obtain, under some restrictions on the characteristic, the local Langlands correspondence for split classical groups over local function fields from the corresponding result of Arthur in characteristic 0.

scholarly journals general linear groups

1997 ◽  
Vol 90 (3) ◽  
pp. 549-576 ◽  
Author(s):  
Avner Ash ◽  
Mark McConnell
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
General Linear Groups
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