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# Complex structure on the smooth dual of GL(n)

Brodzki, Jacek and Plymen, Roger (2002) Complex structure on the smooth dual of GL(n). Documenta Mathematica, 7, 91-112.

Record type: Article

## Abstract

Let G denote the p-adic group GL(n), let ¦(G) denote the smooth dual of G, let ¦(­) denote a Bernstein component of ¦(G) and let H(­) denote a Bernstein ideal in the Hecke algebra H(G). With the aid of Langlands parameters, we equip ¦(­) with the structure of complex algebraic variety, and prove that the periodic cyclic homology of H(­) is isomorphic to the de Rham cohomology of ¦(­). We show how the structure of the variety ¦(­) is related to Xi's a±rmation of a conjecture of Lusztig for GL(n;C). The smooth dual ¦(G) admits a deformation retraction onto the tempered dual ¦t(G)

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Published date: 2002

## Identifiers

Local EPrints ID: 29849
URI: http://eprints.soton.ac.uk/id/eprint/29849
ISSN: 1431-0635

## Catalogue record

Date deposited: 11 May 2006