Note on Cellular Structure of Edge Colored Partition Algebras

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 ${\mathbb{Z}}/r{\...

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Bibliographic Details
Published inKyungpook mathematical journal Vol. 56; no. 3; pp. 669 - 682
Main Authors Kennedy, A. Joseph, Muniasamy, G
Format Journal Article
LanguageKorean
Published 2016
Subjects
Partition algebra
centralizer algebra
direct product
symmetric group
wreath product
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Summary: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 ${\mathbb{Z}}/r{\mathbb{Z}}$-Edge colored partition algebras are quasi-hereditary over a field of characteristic zero which contains a primitive $r^{th}$ root of unity.
Bibliography:KISTI1.1003/JNL.JAKO201631347989439
ISSN:1225-6951
0454-8124