Note on Cellular Structure of Edge Colored Partition Algebras
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In this paper, we study the cellular structure of the $G$-edge colored \linebreak 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 \linebreak a finite cyclic group. Also we prove that the $\mathbb{Z}/r \mathbb{Z}$-Edge colored partition algebras are quasi-hereditary over a field of characteristic zero which contains a primitive $r^{th}$ root of unity.
Abstract
In this paper, we study the cellular structure of the $G$-edge colored \linebreak 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 \linebreak a finite cyclic group. Also we prove that the $\mathbb{Z}/r \mathbb{Z}$-Edge colored partition algebras are quasi-hereditary over a field of characteristic zero which contains a primitive $r^{th}$ root of unity.
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