**Problem of the Week**

**Math Club**

**BUGCAT 2020**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

**BingAWM**

seminars:comb:abstract.201710ska

The (type A) Hecke algebra H_{n}(q) is a certain module over **Z**[q^{1/2}, q^{-1/2}] which is a deformation of the group algebra of the symmetric group. The **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 trace module of the symmetric group algebra. 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, I present a combinatorial formula for the evaluation of traces induced by the sign character at a certain wiring diagram basis of H_{n}(q).

seminars/comb/abstract.201710ska.txt · Last modified: 2020/01/29 14:03 (external edit)

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial-Share Alike 3.0 Unported