Hecke algebras for inner forms of p-adic special linear groups

Aubert, Anne-Marie and Baum, Paul and Plymen, Roger and Solleveld, Maarten (2014) Hecke algebras for inner forms of p-adic special linear groups. [MIMS Preprint]

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Abstract

Let F be a non-archimedean local field and let G^# be the group of F-rational points of an inner form of SL_n. We study Hecke algebras for all Bernstein components of G^#, via restriction from an inner form G of GL_n (F). For any packet of L-indistinguishable Bernstein components, we exhibit an explicit algebra whose module category is equivalent to the associated category of complex smooth G^#-representations. This algebra comes from an idempotent in the full Hecke algebra of G^#, and the idempotent is derived from a type for G. We show that the Hecke algebras for Bernstein components of G^# are similar to affine Hecke algebras of type A, yet in many cases are not Morita equivalent to any crossed product of an affine Hecke algebra with a finite group.

Item Type:	MIMS Preprint
Uncontrolled Keywords:	Representation theory, division algebra, Hecke algebra, types
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups
Depositing User:	Professor Roger Plymen
Date Deposited:	30 Jun 2014
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2153

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