University of Sydney Algebra Seminar

Lewis Dean

Friday 11 September, 12-1pm, in Carslaw 275

Double Affine Coxeter Theory and Affine Quantum Bruhat Graphs

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 \(SL_2\).