|Date: Friday, February 10, 2012
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: W-Cells from Scratch
Abstract: A W-graph is an edge-weighted graph that encodes certain
representations of a Weyl group W or its associated Hecke algebra. In particular, the action of the Hecke algebra by left or right
multiplication on its Kazhdan-Lusztig basis has this form. Knowing
the W-graph makes the computation of Kazhdan-Lusztig polynomials
In this talk we will describe a method, not yet completely effective,
for constructing the (necessarily finite) set of "admissible" W-cells.
This is a class of W-graphs that includes the cells (i.e., strongly
connected components) of the Kazhdan-Lusztig W-graph. For example,
in type A up to rank 9, we know that the only admissible cells are
the K-L cells, but this fails for general W.
Speaker: John Stembridge
Institution: University of Michigan