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Complex structure on the smooth dual of GL(n)

Complex structure on the smooth dual of GL(n)
Complex structure on the smooth dual of GL(n)
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)
1431-0635
91-112
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5

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
PURE UUID: 49b8f35c-67ad-4124-b269-4fd751266d04

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Date deposited: 11 May 2006
Last modified: 25 Nov 2019 19:25

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