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The Hecke algebra of a reductive p-adic group: a geometric conjecture

The Hecke algebra of a reductive p-adic group: a geometric conjecture
The Hecke algebra of a reductive p-adic group: a geometric conjecture
Let H(G) be the Hecke algebra of a reductive p-adic group G. We formulate a conjecture for the ideals in the Bernstein decomposition of H(G). The conjecture says that each ideal is geometrically equivalent to an algebraic variety. Our conjecture is closely related to Lusztig’s conjecture on the asymptotic Hecke algebra. We prove our conjecture for SL(2) and GL(n). We also prove part (1) of the conjecture for the Iwahori ideals of the groups PGL(n) and SO(5). The conjecture, if true, leads to a parametrization of the smooth dual of G by the points in a complex affine locally algebraic variety.
3-8348-0170-4
37
1-34
Vieweg
Aubert, Anne-Marie
f1ab184a-28bd-49a7-bec5-d0abcec2fed0
Baum, Paul
fb630982-847c-4fef-8bd3-b344875be774
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Consani, C.
Marcolli, M.
Aubert, Anne-Marie
f1ab184a-28bd-49a7-bec5-d0abcec2fed0
Baum, Paul
fb630982-847c-4fef-8bd3-b344875be774
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Consani, C.
Marcolli, M.

Aubert, Anne-Marie, Baum, Paul and Plymen, Roger (2006) The Hecke algebra of a reductive p-adic group: a geometric conjecture. In, Consani, C. and Marcolli, M. (eds.) Noncommutative Geometry and Number Theory: Where Arithmetic meets Geometry and Physics. (Vieweg Aspects of Mathematics, , (doi:10.1007/978-3-8348-0352-8_1), 37) Wiesbaden, DE. Vieweg, pp. 1-34. (doi:10.1007/978-3-8348-0352-8_1).

Record type: Book Section

Abstract

Let H(G) be the Hecke algebra of a reductive p-adic group G. We formulate a conjecture for the ideals in the Bernstein decomposition of H(G). The conjecture says that each ideal is geometrically equivalent to an algebraic variety. Our conjecture is closely related to Lusztig’s conjecture on the asymptotic Hecke algebra. We prove our conjecture for SL(2) and GL(n). We also prove part (1) of the conjecture for the Iwahori ideals of the groups PGL(n) and SO(5). The conjecture, if true, leads to a parametrization of the smooth dual of G by the points in a complex affine locally algebraic variety.

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Published date: 2006
Organisations: Pure Mathematics

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Local EPrints ID: 359947
URI: http://eprints.soton.ac.uk/id/eprint/359947
ISBN: 3-8348-0170-4
PURE UUID: 154d8bb7-3e8d-437d-b6e7-9a708b8a577e

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Date deposited: 19 Nov 2013 13:50
Last modified: 09 Jul 2020 16:31

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