SMS scnews item created by Kevin Coulembier at Mon 6 Jun 2016 1353
Type: Seminar
Distribution: World
Expiry: 18 Jul 2016
Calendar1: 17 Jun 2016 1200-1300
CalLoc1: Carslaw 375
CalTitle1: Combinatorics of affine Springer fibres
Auth: kevinc@pkevinc.pc (assumed)

# Algebra Seminar: Ram -- Combinatorics of affine Springer fibres

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.


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