Generalized Temperley-Lieb algebras for imprimitive reflection groups

In this talk, I will introduce our newly defined Temperley-Lieb algebra $TL_{r,p,n}$ corresponding to an imprimitive unitary reflection group $G(r,p,n)$. The Temperley-Lieb algebra $TL_n(q)$ is a quotient of the Hecke algebra $H_n(q)$ of type $A_{n-1}$. It plays a pivotal role in the polynomial invariant of knots and links. As a generalization, our Temperley-Lieb algebra $TL_{r,p,n}$ is defined as a quotient of the cyclotomic Hecke algebra $H(r,p,n)$. The generalized algebra $TL_{r,p,n}$ is cellular, and I'll give the decomposition matrix of it using the cellular basis.