## Discrete Geometry and Combinatorics Seminar

Mark SkanderaLehigh University
Evaluations of Hecke algebra traces at the wiring diagram basis
Monday, October 16, 2017 - 2:30pm
Malott 206

The (type A) Hecke algebra $H_n(q)$ is a certain module over $\mathbb Z[q^{1/2},q^{-1/2}]$ which is a deformation of the group algebra of the symmetric group. The $\mathbb Z[q^{1/2},q^{-1/2}]$-module of its trace functions has rank equal to the number of integer partitions of $n$, and has bases which are natural deformations of those of the symmetric group algebra trace module. While no known closed formulas give the evaluation of these traces at the natural basis elements of $H_n(q)$, or at the Kazhdan-Lusztig basis, we present a combinatorial formulas for the evaluation of induced sign character traces at a certain wiring diagram basis of $H_n(q)$.