Algebra Seminar: Howse -- Invariants of Kazhdan-Lusztig cells

Edmund Howse (National University of Singapore) 

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

Title: Invariants of Kazhdan-Lusztig cells 

Abstract: 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 tau-invariant. In this talk, we
discuss invariants such as the Vogan classes of Bonnafe 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.