Combinatorics Seminar: Combinatorial evaluation of Hecke algebra traces

Seminar | April 24 | 11:10 a.m.-12 p.m. | 939 Evans Hall

 Mark Skandera, Lehigh University

 Department of Mathematics

(Please note the unusual time of this talk.)

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 formulas give the evaluation of these traces at the natural basis elements of $H_n(q)$, there are some nice combinatorial formulas for the evaulation of certain traces at certain Kazhdan-Lusztig basis elements. We will also discuss the open problem of evaluating these traces at other basis elements.