Algebra Seminar: Dean -- Double Affine Coxeter Theory and Affine Quantum Bruhat Graphs

Speaker: Lewis Dean (University of Glasgow) 

When/Where: Friday 11 September, 12-1pm, in Carslaw 275 

Title: Double Affine Coxeter Theory and Affine Quantum Bruhat Graphs 

Abstract: Kac-Moody Hecke algebras have a basis indexed by their underlying Weyl group.
By affinising certain classes of these Hecke algebras, we obtain an algebra indexed
by​ a double affine Weyl (semi)group.  Although such Weyl groups are not Coxeter
groups, much work has been done to give them Coxeter-like structures, including a length
function and a Bruhat order.  One further structure we want to develop for them is the
Demazure product, which describes multiplication in the q=0 specialisation of its
corresponding Kac-Moody Affine Hecke algebra.  In this talk, we discuss conjectures on
generalising an approach developed by F.  Schremmer using the quantum Bruhat graph, and
results so far on using this as a definition in the double affine setting, particularly
in type SL_2.