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 Thiéry on affine crystals arising from promotion operators. Finally, we give a computer implementation of Stembridge's local axioms for simply-laced crystal bases.
|Commitee:||Kuperberg, Greg, Thiery, Nicolas M., Vazirani, Monica|
|School:||University of California, Davis|
|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|
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