The Hecke algebra of a reductive p -adic group: a geometric conjecture
Identifieur interne : 000B16 ( Main/Merge ); précédent : 000B15; suivant : 000B17The Hecke algebra of a reductive p -adic group: a geometric conjecture
Auteurs : Anne-Marie Aubert [France] ; Paul Baum [États-Unis] ; Roger Plymen [Royaume-Uni]Source :
- Aspects of Mathematics [ 0179-2156 ] ; 2006.
Abstract
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.
Url:
DOI: 10.1007/978-3-8348-0352-8_1
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<front><div type="abstract" xml:lang="en">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.</div>
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