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Dissertation/Thesis Abstract

Excursions into Algebra and Combinatorics at q = 0
by Denton, Tom, Ph.D., University of California, Davis, 2011, 140; 3482117
Abstract (Summary)

We explore combinatorics associated with the degenerate Hecke algebra at q = 0, obtaining a formula for a system of orthogonal idempotents, and also exploring various pattern avoidance results. Generalizing constructions for the 0-Hecke algebra, we explore the representation theory of [special characters omitted]-trivial monoids.

We then discuss two-tensors of crystal bases for Uq([special characters omitted]), establishing a complementary result to one of Bandlow, Schilling, and ThiƩry on affine crystals arising from promotion operators. Finally, we give a computer implementation of Stembridge's local axioms for simply-laced crystal bases.

Indexing (document details)
Advisor: Schilling, Anne
Commitee: Kuperberg, Greg, Thiery, Nicolas M., Vazirani, Monica
School: University of California, Davis
Department: Mathematics
School Location: United States -- California
Source: DAI-B 73/03, Dissertation Abstracts International
Subjects: Mathematics, Theoretical Mathematics
Keywords: Algebra, Combinatorics, Crystal bases, Hecke algebra, Pattern avoidance, Representation theory
Publication Number: 3482117
ISBN: 978-1-267-02332-2
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