Kazhdan-Lusztig theory and p-adic groups

Stefan Dawydiak (University of Glasgow)

Wednesday 1st October 16:00-17:00
Maths 311B

Abstract

Hecke algebras are certain deformations of group rings that
can convert infinite-dimensional problems in representation theory to
families of finite-dimensional problems. Starting from the celebrated
work of Kazhdan-Lusztig, rich geometric and spectral pictures of the
Hecke algebras associated to affine Weyl groups have emerged as a
special case of the Local Langlands Correspondence for p-adic groups. I
will report on work, initiated by Braverman-Kazhdan, to extend these
pictures to a slightly larger algebra, Lusztig's asymptotic Hecke algebra.

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