English

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}
}