Note on Cellular Structure of Edge Colored Partition Algebras

Abstract

In this paper, we study the cellular structure of the G-edge colored partition algebras, when G is a finite group. Further, we classified all the irreducible representations of these algebras using their cellular structure whenever G is a finite cyclic group. Also we prove that the Z/rZ-Edge colored partition algebras are quasi-hereditary over a field of characteristic zero which contains a primitive r root of unity.