Type: Seminar

Distribution: World

Expiry: 18 Jul 2016

CalTitle1: Combinatorics of affine Springer fibres

Auth: kevinc@pkevinc.pc (assumed)

This is the third lecture in a series of 3 by Arun Ram (University of Melbourne), the other two are on June 14 and 16. Friday 17 June, 12-1pm, Place: Carslaw 375 Combinatorics of affine Springer fibres This talk will be a survey of the relation between affine Springer fibres and representations of the double affine Hecke algebra. I will likely focus on a favourite example of the elliptic homogeneous case where I can draw a nice picture illustrating how the affine Springer fibre is decomposed into cells indexed by connected components of complement of a hyperplane arrangement called the Shi arrangement (the same one that appears in the K-theory version of the Chevalley-Shephard-Todd theorem for reflection groups). These regions then correspond to a Macdonald polynomial basis of the corresponding representation of the double affine Hecke algebra.