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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