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On L-packets and depth for SL_2(K) and its inner form

On L-packets and depth for SL_2(K) and its inner form
On L-packets and depth for SL_2(K) and its inner form
We consider the group SL_2(K), where K is a local non-archimedean field of characteristic two. We prove that the depth of any irreducible representation of SL_2 (K) is larger than the depth of the corresponding Langlands parameter, with equality if and only if the L-parameter is essentially tame.

We also work out a classification of all L-packets for SL_2 (K) and for its non-split inner form, and we provide explicit formulae for the depths of their L-parameters.

1793-0421
1-19
Aubert, Anne-Marie
f1ab184a-28bd-49a7-bec5-d0abcec2fed0
Mendes, Sergio
15127dc1-4f31-4609-a7c5-0fd10df6da08
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Solleveld, Maarten
87e40b53-0137-45fd-8582-38da531528a4
Aubert, Anne-Marie
f1ab184a-28bd-49a7-bec5-d0abcec2fed0
Mendes, Sergio
15127dc1-4f31-4609-a7c5-0fd10df6da08
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Solleveld, Maarten
87e40b53-0137-45fd-8582-38da531528a4

Aubert, Anne-Marie, Mendes, Sergio, Plymen, Roger and Solleveld, Maarten (2017) On L-packets and depth for SL_2(K) and its inner form. International Journal of Number Theory, 1-19. (doi:10.1142/S1793042117501421).

Record type: Article

Abstract

We consider the group SL_2(K), where K is a local non-archimedean field of characteristic two. We prove that the depth of any irreducible representation of SL_2 (K) is larger than the depth of the corresponding Langlands parameter, with equality if and only if the L-parameter is essentially tame.

We also work out a classification of all L-packets for SL_2 (K) and for its non-split inner form, and we provide explicit formulae for the depths of their L-parameters.

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More information

Accepted/In Press date: 20 December 2016
e-pub ahead of print date: 7 July 2017
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 369683
URI: https://eprints.soton.ac.uk/id/eprint/369683
ISSN: 1793-0421
PURE UUID: cd26f9d8-54e2-4252-8355-e78e266779b5

Catalogue record

Date deposited: 09 Oct 2014 12:25
Last modified: 18 Jul 2019 14:23

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