"A Recursive Structure on Bruhat Intervals"

DJ Wells
University of Kentucky

Monday, December 3, 2007
4:00 pm, 113 Patterson Office Tower

Abstract:

Given a group whose generators are involutions (such as a symmetric group) we can define a partial order on the group elements by defining one element to be less than another if, when both are written as reduced words on the generators, the one is a subword of the other. This is called the Bruhat order.

In a paper based largely on his doctoral thesis, Nathan Reading gives a structural recursion on intervals in Bruhat order. This structural recursion gives a new proof that (the order complex of) open Bruhat intervals are always PL Spheres and also leads to a recursive formula for the cd-indices of Bruhat intervals.

I will outline some requisite background concepts, then present the recursion, given in terms of the operations of forming a pyramid, shaving, and zipping, and gives some consequences of this structure, including a recursion on the cd-indices.