The local Langlands correspondence for inner forms of SL_n

Plymen, Roger (2013) The local Langlands correspondence for inner forms of SL_n. In: Warwick Number Theory Symposium 2012-2013, 29 Apr - 03 May 2013, University of Warwick, UK. (Unpublished)

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Abstract

This is a beamer presentation of MIMS eprint 2013.38 of the same title (joint authors are A-M. Aubert, P. Baum, R. Plymen, M. Solleveld). 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:	Conference or Workshop Item (Lecture)
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:	01 Aug 2013
Last Modified:	20 Oct 2017 14:13
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2011

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