Last updated: 26 March 2015
It has been a joy to develop these results while participating in Lie theory group at the University of Wisconsin-Madison. Georgia Benkart and Paul Terwilliger have been particularly helpful with advice and mathematical ideas, and I enjoyed many discussions with Stephen Griffeth, Michael Lau, and Matt Ondrus (among others).
I am especially grateful to my advisor Arun Ram, whose insights, encouragement and patient help guided me into the world of representation theory, and taught me how to talk, write, and research in the world of mathematics.
Some grants also supported this research, offering extra time for research (VI-GRE DMS-9819788) and funds to travel and interact with other communities (NSF DMS-0097977, NSA MDA904-01-1-0032).
Lastly, throughout all the difficulties and stresses of a doctoral program my wife Claudia has been (and continues to be) an invaluable companion.
This is an excerpt of the PhD thesis Unipotent Hecke algebras: the structure, representation theory, and combinatorics by F. Nathaniel Edgar Thiem.