Cyclotomic Temperley-Lieb algebra of type D and its representation theory
Rings and Algebras
2010-11-23 v2
Abstract
We define a new class of algebras, cyclotomic Temperley-Lieb algebras of type D, in a diagrammatic way, which is a generalization of Temperley-Lieb algebras of type D. We prove that the cyclotomic Temperley-Lieb algebras of type D are cellular. In fact, an explicit cellular basis is given by means of combinatorial methods. After determining all the irreducible representations of these algebras, we give a necessary and sufficient condition for a cyclotomic Temperley-Lieb algebra of type D to be quasi-hereditary.
Keywords
Cite
@article{arxiv.1011.4089,
title = {Cyclotomic Temperley-Lieb algebra of type D and its representation theory},
author = {Jie Sun},
journal= {arXiv preprint arXiv:1011.4089},
year = {2010}
}