Excursions into Algebra and Combinatorics at $q=0$
Skip to main content
Open Access Publications from the University of California

Department of Mathematics

Graduate bannerUC Davis

Excursions into Algebra and Combinatorics at $q=0$

Published Web Location

No data is associated with this publication.

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 $\JJ$-trivial monoids. We then discuss two-tensors of crystal bases for $U_q(\tilde{\mathfrak{sl}_2})$, 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.

Item not freely available? Link broken?
Report a problem accessing this item