The Hecke algebra of a reductive p -adic group: a geometric conjecture
Identifieur interne : 000B07 ( Main/Exploration ); précédent : 000B06; suivant : 000B08The 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
Affiliations:
- France, Royaume-Uni, États-Unis
- Angleterre, Pennsylvanie, Île-de-France
- Paris, University Park (Pennsylvanie)
- Université d'État de Pennsylvanie
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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></front></TEI><affiliations><list><country><li>France</li><li>Royaume-Uni</li><li>États-Unis</li></country><region><li>Angleterre</li><li>Pennsylvanie</li><li>Île-de-France</li></region><settlement><li>Paris</li><li>University Park (Pennsylvanie)</li></settlement><orgName><li>Université d'État de Pennsylvanie</li></orgName></list><tree><country name="France"><region name="Île-de-France"><name sortKey="Aubert, Anne Marie" sort="Aubert, Anne Marie" uniqKey="Aubert A" first="Anne-Marie" last="Aubert">Anne-Marie Aubert</name></region><name sortKey="Aubert, Anne Marie" sort="Aubert, Anne Marie" uniqKey="Aubert A" first="Anne-Marie" last="Aubert">Anne-Marie Aubert</name></country><country name="États-Unis"><region name="Pennsylvanie"><name sortKey="Baum, Paul" sort="Baum, Paul" uniqKey="Baum P" first="Paul" last="Baum">Paul Baum</name></region><name sortKey="Baum, Paul" sort="Baum, Paul" uniqKey="Baum P" first="Paul" last="Baum">Paul Baum</name></country><country name="Royaume-Uni"><region name="Angleterre"><name sortKey="Plymen, Roger" sort="Plymen, Roger" uniqKey="Plymen R" first="Roger" last="Plymen">Roger Plymen</name></region><name sortKey="Plymen, Roger" sort="Plymen, Roger" uniqKey="Plymen R" first="Roger" last="Plymen">Roger Plymen</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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