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Kyungpook Mathematical Journal -0001; 56(3): 669-682

Published online November 30, -0001

Copyright © Kyungpook Mathematical Journal.

Note on Cellular Structure of Edge Colored Partition Algebras

A. Joseph Kennedy1, G. Muniasamy2

Department of Mathematics, Pondicherry University, Pondicherry, India1
Department of Mathematics, MIT, Anna University, Chennai, India2

Received: March 24, 2014; Accepted: February 21, 2015

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 rth root of unity.

Keywords: Partition algebra, centralizer algebra, direct product, wreath product, symmetric group.