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 Bn with respect to two different choices of weight function.