OIST Representation Theory Seminar

Speaker: Tianyuan Xu, University of Colorado at Boulder

Title: 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.

Zoom info can be found on the seminar webpage.