A Cellular Basis Of Cyclotomic Temperley-Lieb

Cyclotomic Temperley-Lieb algebras [4] are generalization of Temperley-Lieb [6]. These algebras can be defined in terms of generators and relations. They can also be reformulated geometrically by labelled Temperley-Lieb diagrams. Motivated by J.Eyang's work [1] on the Temperley-Lieb algebras, we will construct a cellular basis for cyclotomic Temperley-Lieb algebra in the sense of [2] by using its generators and relations. Via such a basis, we will give another proof of the Branching rule on the cell module [4].