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.