The quasi-partition algebra

JOURNAL OF ALGEBRA

卷:404

Article

Daugherty, Zajj¹  Orellana, Rosa¹ 

[1] Dartmouth Coll, Dept Math, Hanover, NH 03755 USA

关键词: Representation theory;    Partition algebras;    Diagram algebras;    Centralizer algebras;    Schur-Weyl duality;   

DOI  :  10.1016/j.jalgebra.2013.11.028

来源: Elsevier

【 摘 要 】

We introduce the quasi-partition algebra QP(k) (n) as a centralizer algebra of the symmetric group. This algebra is a sub-algebra of the partition algebra and inherits many similar combinatorial properties. We construct a basis for QP(k)(n), give a formula for its dimension in terms of the Bell numbers, and describe a set of generators for QP(k) (n) as a complex algebra. In addition, we give the dimensions and indexing set of its irreducible representations. We also provide the Bratteli diagram for the tower of quasi-partition algebras (constructed by letting k range over the positive integers). (c) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free