2011/08/22 by Tom Denton, Denton, Tom
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.CO #math.QA #math.RT #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1108.4379
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
arxiv created 2011/08/22 · openalex publication_date 2011/08/22 · arxiv updated 2012/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Uq(\mathfraksl2), 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.