Quasi-partition algebra
Representation Theory
2012-12-12 v1 Combinatorics
Abstract
We introduce the quasi-partition algebra as a centralizer algebra of the symmetric group. This algebra is a subalgebra of the partition algebra and inherits many similar combinatorial properties. We construct a basis for , give a formula for its dimension in terms of the Bell numbers, and describe a set of generators for 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 range over the positive integers).
Cite
@article{arxiv.1212.2596,
title = {Quasi-partition algebra},
author = {Zajj Daugherty and Rosa Orellana},
journal= {arXiv preprint arXiv:1212.2596},
year = {2012}
}