The local Langlands correspondence for inner forms of SL_n

Aubert, Anne-Marie and Baum, Paul and Plymen, Roger and Solleveld, Maarten (2013) The local Langlands correspondence for inner forms of SL_n. [MIMS Preprint]

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Abstract

Let $F$ be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group $SL_n (F)$. It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for $SL_n (F)$ 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 $SL_n (F)$. An analogous result is shown in the archimedean case. 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 $GL_n (F)$, when the fields are close enough compared to the depth of the representations.

Item Type: MIMS Preprint
Uncontrolled Keywords: representation theory, local Langlands conjecture, division algebra, close fields
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theory
MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups
Depositing User: Professor Roger Plymen
Date Deposited: 23 Jul 2013
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1998

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