On Kazhdan–Lusztig cells of a-value 2

Abstract: The Kazhdan–Lusztig (KL) cells of a Coxeter group are subsets of the group defined using the KL basis of the associated Iwahori–Hecke algebra. The cells of symmetric groups can be computed via the Robinson–Schensted correspondence, but for general Coxeter groups combinatorial descriptions of KL cells are largely unknown except for cells of a-value 0 or 1, where a refers to an N-valued function defined by Lusztig that is constant on each cell. In this talk, we will report some recent progress on KL cells of a-value 2. In particular, we classify Coxeter groups with finitely many elements of a-value 2, and for such groups we characterize and count all cells of a-value 2 via certain posets called heaps. We will also mention some applications of these results for cell modules. This is joint work with Richard Green.

combinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

OIST representation theory seminar

Series comments: Timings of this seminar may vary from week to week.