Date of Award

9-2013

Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Mathematics

First Advisor

Eric Sommers

Second Advisor

Tom Braden

Third Advisor

Julianna Tymoczko

Subject Categories

Mathematics

Abstract

This thesis deals with the study of Schubert varieties, which are subsets of flag varieties indexed by elements of Weyl groups. We start by defining Lascoux elements in the Hecke algebra, and showing that they coincide with the Kazhdan-Lusztig basis elements in certain cases. We then construct a resolution (Zw, π) of the Schubert variety Xw for which *(C[l(w)]) is a sheaf on Xw whose expression in the Hecke algebra is closely related to the Lascoux element. We also define two new polynomials which coincide with the intersection cohomology Poincar\'e polynomial in certain cases. In the final chapter, we discuss some interesting combinatorial results concerning Bell and Catalan numbers which arose throughout the course of this work.

Included in

Mathematics Commons

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