Date of Award
9-2013
Document type
dissertation
Access 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 Rπ*(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.
DOI
https://doi.org/10.7275/fqca-ea47
Recommended Citation
Koonz, Jennifer, "Properties of Singular Schubert Varieties" (2013). Open Access Dissertations. 839.
https://doi.org/10.7275/fqca-ea47
https://scholarworks.umass.edu/open_access_dissertations/839