Excursions into Algebra and Combinatorics at $q=0$

Tom Denton

Excursions into Algebra and Combinatorics at $q=0$

Representation Theory 2012-04-24 v1 Combinatorics Quantum Algebra

Authors: Tom Denton

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 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.

Keywords

hecke algebra crystal bases quantum group representations

Cite

@article{arxiv.1108.4379,
  title  = {Excursions into Algebra and Combinatorics at $q=0$},
  author = {Tom Denton},
  journal= {arXiv preprint arXiv:1108.4379},
  year   = {2012}
}

Comments

92 pages, 13 figures. PHd Dissertation accepted at the University of California on July 15th, 2011. arXiv admin note: text overlap with arXiv:1012.1361

Excursions into Algebra and Combinatorics at $q=0$

Abstract

Keywords

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