Algebra Seminar: Thomas -- Trivial Kazhdan-Lusztig polynomials and cubulation of the Bruhat graph

Anne Thomas (University of Sydney) will be speaking in the algebra seminar.  We will go
out for lunch after the talk---all are welcome to join! 

When: 12-1pm Friday August 29 

Where: Carslaw 175 

Title: Trivial Kazhdan-Lusztig polynomials and cubulation of the Bruhat graph 

Abstract: Let (W,S) be any Coxeter system and let y be any element of W. We
investigate the relationship between the condition that the Kazhdan-Lusztig polynomial
P_{x,y} is trivial for all x less than or equal to y in Bruhat order, and the condition
that the Bruhat graph for the interval [1,y] can be cubulated, meaning roughly that this
graph can be spanned by a product of subintervals of the integers. In one direction, we
combine results of Carrell-Peterson and Elias-Williamson to prove that if the Bruhat
graph for [1,y] can be cubulated, then P_{x,y} = 1 for all x \leq y. We then consider
the converse, using word combinatorics in Coxeter groups, methods from geometric group
theory, and computer experiments.  We establish that the converse is not true in some
exceptional types, but it is true in many other cases.