Type $\tilde{C}$ Temperley-Lieb algebra quotients and Catalan combinatorics
Combinatorics
2019-04-18 v1 Rings and Algebras
Representation Theory
Abstract
We study some algebraic and combinatorial features of two algebras that arise as quotients of Temperley-Lieb algebras of type , namely, the two-boundary Temperley-Lieb algebra and the symplectic blob algebra. We provide a monomial basis for both algebras. The elements of these bases are parameterized by certain subsets of fully commutative elements. We enumerate these elements according to their affine length.
Cite
@article{arxiv.1904.08351,
title = {Type $\tilde{C}$ Temperley-Lieb algebra quotients and Catalan combinatorics},
author = {Sadek Al Harbat and Camilo González and David Plaza},
journal= {arXiv preprint arXiv:1904.08351},
year = {2019}
}
Comments
34 pages, many figures