Murnaghan-Kirillov theory for supercuspidal representations of tame general linear groups

2004 ◽  
Vol 2004 (575) ◽  
pp. 1-35 ◽  
Author(s):  
J. D. Adler ◽  
S. DeBacker
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
Supercuspidal Representations ◽  
General Linear Groups ◽  
Kirillov Theory

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 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

scholarly journals Restriction for general linear groups: The local non-tempered Gan–Gross–Prasad conjecture (non-Archimedean case)

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kei Yuen Chan
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
Branching Laws ◽  
General Linear Groups ◽  
Branching Law

Abstract We prove a local Gan–Gross–Prasad conjecture on predicting the branching law for the non-tempered representations of general linear groups in the case of non-Archimedean fields. We also generalize to Bessel and Fourier–Jacobi models and study a possible generalization to Ext-branching laws.

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