## 2011.92: The representation theory of p-adic GL(n) and Deligne-Langlands parameters

2011.92:
J.E. Hodgins and Roger Plymen
(1996)
*The representation theory of p-adic GL(n) and Deligne-Langlands parameters.*
In:
Rajendra Bhatia, (eds).
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 |
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Uncontrolled Keywords: | General linear group, p-adic field, extended quotient |

Subjects: | MSC 2000 > 20 Group theory and generalizations MSC 2000 > 22 Topological groups, Lie groups |

MIMS number: | 2011.92 |

Deposited By: | Professor Roger Plymen |

Deposited On: | 16 November 2011 |

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