On L-packets and depth for SL2(K) and its inner form-Reference-Cited by-同舟云学术

On L-packets and depth for SL2(K) and its inner form

Published:2017-10-16 Issue:10 Volume:13 Page:2545-2568
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Aubert Anne-Marie¹,Mendes Sergio²,Plymen Roger³,Solleveld Maarten⁴

Affiliation:

1. Institut de Mathématiques de Jussieu, Paris Rive Gauche, U.M.R. 7586 du C.N.R.S., U.P.M.C., 4 Place Jussieu 75005, Paris, France

2. ISCTE - Lisbon University Institute, Av. das Forças Armadas, 1649-026, Lisbon, Portugal

3. School of Mathematics, Southampton University, Southampton SO17 1BJ, UK

4. IMAPP, Radboud Universiteit, Heyendaalseweg 135, 6525AJ, Nijmegen, The Netherlands

Abstract

We consider the group [Formula: see text], where [Formula: see text] is a local non-archimedean field of characteristic two. We prove that the depth of any irreducible representation of [Formula: see text] is larger than the depth of the corresponding Langlands parameter, with equality if and only if the [Formula: see text]-parameter is essentially tame. We also work out a classification of all [Formula: see text]-packets for [Formula: see text] and for its non-split inner form, and we provide explicit formulae for the depths of their [Formula: see text]-parameters.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042117501421

Reference16 articles.

1. Depth and the Local Langlands Correspondence

2. The local Langlands correspondence for inner forms of SL$$_{n}$$

3. The Local Langlands Conjecture for GL(2)

4. The essentially tame local Langlands correspondence, III: the general case

5. The Admissible Dual of SL(N ) II

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