Generalised Temperley-Lieb algebras of type $G(r,1,n)$

TL;DR

This paper introduces a new class of algebras generalizing Temperley-Lieb algebras for type G(r,1,n), establishing their cellular structure and analyzing their decomposition matrices using KLR algebra techniques.

Contribution

It defines a quotient of cyclotomic Hecke algebras as a generalized Temperley-Lieb algebra and determines its cellular structure and decomposition matrix.

Findings

Established graded cellular structure for the algebra

Determined the decomposition matrix using KLR algebra technology

Generalized Temperley-Lieb algebras for type G(r,1,n)

Abstract

In this paper, we define a quotient of the cyclotomic Hecke algebra of type $G(r,1,n)$ as a generalisation of the Temperley-Lieb algebras of type $A$ and $B$. We establish a graded cellular structure for the generalised Temperley-Lieb algebra and, using the technology of $KLR$ algebras, determine the corresponding decomposition matrix.