Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 Fall 2017

Speaker:  Mark Skandera, Lehigh University
Title: Evaluations of Hecke algebra traces at the wiring diagram basis
Time: 2:30 PM, Monday, October 16, 2017
Place:  Malott 206

Abstract: 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 $H_n(q)$.

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