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arXiv · 1108.4379

Excursions into Algebra and Combinatorics at $q=0$

Tom Denton
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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 $\JJ$-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 Thiéry 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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Tom Denton. 2011-08-22. Excursions into Algebra and Combinatorics at $q=0$. https://arxiv.org/abs/1108.4379

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