Cyclotomic Temperley-Lieb algebra of type D and its representation theory
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2010
- DOI:
- 10.48550/arXiv.1011.4089
- arXiv:
- arXiv:1011.4089
- Bibcode:
- 2010arXiv1011.4089S
- Keywords:
-
- Mathematics - Rings and Algebras;
- 16G30;
- 20G05;
- 57M25
- E-Print:
- Communications in Algebra, 38, (2010), 94-118