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)
91-112
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
2002
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, .
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: 16 Mar 2024 03:24
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