Jones--Wenzl projections and Dyck tilings: type $A$ and $B$
Combinatorics
2024-02-16 v1 Statistical Mechanics
Mathematical Physics
math.MP
Quantum Algebra
Abstract
The Jones--Wenzl projections are a special class of elements of the Temperley--Lieb algebra. We prove that the coefficient appearing in the Jones--Wenzl projection is given by a generating function of combinatorial objects, called Dyck tilings. We also show that this correspondence holds for type case.
Keywords
Cite
@article{arxiv.2402.09887,
title = {Jones--Wenzl projections and Dyck tilings: type $A$ and $B$},
author = {Keiichi Shigechi},
journal= {arXiv preprint arXiv:2402.09887},
year = {2024}
}
Comments
12 pages