Plethysm and the algebra of uniform block permutations
Combinatorics
2022-11-15 v2 Representation Theory
Abstract
We study the representation theory of the uniform block permutation algebra in the context of the representation theory of factorizable inverse monoids. The uniform block permutation algebra is a subalgebra of the partition algebra and is also known as the party algebra. We compute its characters and provide a Frobenius characteristic map to symmetric functions. This reveals connections of the characters of the uniform block permutation algebra and plethysms of Schur functions.
Keywords
Cite
@article{arxiv.2112.13909,
title = {Plethysm and the algebra of uniform block permutations},
author = {Rosa Orellana and Franco Saliola and Anne Schilling and Mike Zabrocki},
journal= {arXiv preprint arXiv:2112.13909},
year = {2022}
}
Comments
45 pages; incorporated comments by referee, corrected character tables in Section 5