Excursions into Algebra and Combinatorics at q=0
Abstract
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 -trivial monoids. We then discuss two-tensors of crystal bases for Uq(sl2), establishing a complementary result to one of Bandlow, Schilling, and Thi\'ery on affine crystals arising from promotion operators. Finally, we give a computer implementation of Stembridge's local axioms for simply-laced crystal bases.
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