The representation theory of p-adic GL(n) and Deligne-Langlands parameters

Hodgins, J.E. and Plymen, Roger (1996) The representation theory of p-adic GL(n) and Deligne-Langlands parameters. In: Analysis, Geometry and Probability. Texts and Readings in Mathematics, 10 . Hindustan book agency, India, pp. 54-72. ISBN 81 85931 12 7

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Abstract

Let GL(n) denote the general linear group over a local nonarchimedean field. For the equivalence classes of irreducible smooth representations of GL(n) admitting nonzero Iwahori fixed vectors, we have the classical Deligne-Langlands parameters. We prove that the Deligne-Langlands parameters have a definite geometric structure: the structure of the extended quotient of a complex torus of dimension n by the symmetric group S_n. Notes: 1. At the time of publication, the extended quotient was called the Brylinski quotient. 2. We say in the Introduction that this chapter is a "re-interpretation" of [8]. Reference [8] was, however, never published, so this eprint is now the primary source: the book itself is out of print. 3. The main result in this chapter is the precursor of a wide-ranging geometric conjecture, in the representation theory of p-adic groups, developed by Anne-Marie Aubert, Paul Baum and myself in a series of papers from 2007 -- 2011.

Item Type:	Book Section
Uncontrolled Keywords:	General linear group, p-adic field, extended quotient
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:	16 Nov 2011
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1697

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