Tuesday, December 7, 16:00 (!)

Bridget Tenner (DePaul University), Combinatorics, grades, and Lusztig's a-function.

Abstract:
In recent work, we showed that the grades of simple modules indexed by boolean permutations, over the incidence algebra of the symmetric group with respect to the Bruhat order, are given by Lusztig's a-function. The argument was combinatorial, relying on properties of reduced words and boolean ideals. In this talk, we will discuss that combinatorics. We will relate reduced words, boolean intersections, and a permutation's shape under the Robinson-Schensted correspondence -- all in the context of grades and the a-function. As part of this, we will give combinatorial meaning to the length of the second row of these permutations' shapes.
This work is joint with Volodymyr Mazorchuk