arXiv:1108.4379 Abstract | arXiv Analytics

arXiv:1108.4379 [math.RT]Abstract References Reviews Resources

Excursions into Algebra and Combinatorics at $q=0$

Published 2011-08-22Version 1

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.

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

Categories: math.RT, math.CO, math.QA

Keywords: combinatorics, excursions, degenerate hecke algebra, stembridges local axioms, computer implementation

Tags: dissertation

Related articles: Most relevant | Search more

arXiv:2004.08033 [math.RT] (Published 2020-04-17)

Combinatorics of Type D Exceptional Sequences

Emily Carrick, Alexander Garver

arXiv:1905.00613 [math.RT] (Published 2019-05-02)

Combinatorics of faithfully balanced modules

William Crawley-Boevey, Biao Ma, Baptiste Rognerud, Julia Sauter

arXiv:math/0604333 [math.RT] (Published 2006-04-14)

Combinatorics of $A_2$-crystals