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

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

2005-02-11

arxiv.org/abs/math/0502234v3

Mathematics

Representation Theory

45 pages

Scientific paper

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 our conjecture for the Iwahori ideals of the groups PGL(n) and SO(5).

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