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The local Langlands correspondence for inner forms of SL_n

The local Langlands correspondence for inner forms of SL_n
The local Langlands correspondence for inner forms of SL_n
Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group SLn(F). It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for SLn(F) enhanced with an irreducible representation of an S-group and, on the other hand, the union of the spaces of irreducible admissible representations of all inner forms of SLn(F) up to equivalence. An analogous result is shown in the archimedean case. For p-adic fields this is based on the work of Hiraga and Saito. To settle the case where F has positive characteristic, we employ the method of close fields. We prove that this method is compatible with the local Langlands correspondence for inner forms of GLn(F), when the fields are close enough compared to the depth of the representations.
2197-9847
Aubert, Anne-Marie
f1ab184a-28bd-49a7-bec5-d0abcec2fed0
Baum, Paul
fb630982-847c-4fef-8bd3-b344875be774
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Solleveld, Maarten
87e40b53-0137-45fd-8582-38da531528a4
Aubert, Anne-Marie
f1ab184a-28bd-49a7-bec5-d0abcec2fed0
Baum, Paul
fb630982-847c-4fef-8bd3-b344875be774
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Solleveld, Maarten
87e40b53-0137-45fd-8582-38da531528a4

Aubert, Anne-Marie, Baum, Paul, Plymen, Roger and Solleveld, Maarten (2016) The local Langlands correspondence for inner forms of SL_n. Research in the Mathematical Sciences, 3, [32]. (doi:10.1186/s40687-016-0079-4).

Record type: Article

Abstract

Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group SLn(F). It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for SLn(F) enhanced with an irreducible representation of an S-group and, on the other hand, the union of the spaces of irreducible admissible representations of all inner forms of SLn(F) up to equivalence. An analogous result is shown in the archimedean case. For p-adic fields this is based on the work of Hiraga and Saito. To settle the case where F has positive characteristic, we employ the method of close fields. We prove that this method is compatible with the local Langlands correspondence for inner forms of GLn(F), when the fields are close enough compared to the depth of the representations.

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Accepted/In Press date: 2 August 2016
e-pub ahead of print date: 5 December 2016
Published date: 5 December 2016
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 369681
URI: http://eprints.soton.ac.uk/id/eprint/369681
ISSN: 2197-9847
PURE UUID: 7500c973-24c6-440f-bf26-5c19de7f8bc6

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Date deposited: 09 Oct 2014 12:16
Last modified: 16 Dec 2019 20:22

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