## University of Sydney Algebra Seminar

# Edmund Howse (National University of Singapore)

## Friday 10 August, 12-1pm, Place: Carslaw 375

## Invariants of Kazhdan–Lusztig cells

Lusztig has described the partition of a Coxeter group *W*
into left, right and two-sided cells with respect to a weight function. This
description relies on certain equivalence relations that are calculated in
the corresponding Iwahori–Hecke algebra *H*, and the resulting cells afford
representations of both *W* and *H*.

As cells are difficult to calculate directly from the definition, invariants
of cells are sought after to make it possible to determine cells purely at the
level of the Coxeter group. For instance, a classical result of Kazhdan and
Lusztig is that the left cells of the symmetric group are characterised by the
generalised τ-invariant.

In this talk, we discuss invariants such as the Vogan classes of Bonnafé
and Geck and introduce a modified version of the right descent set. We then
describe how a combination of these concepts leads to a characterisation of
the left cells in type *B _{n}* with respect to two different choices of weight function.