Plethysm and the algebra of uniform block permutations

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.

45 pages; incorporated comments by referee, corrected character tables in Section 5

Cited by in corpus (3)

• Transition matrices and Pieri-type rules for polysymmetric functions
• The lattice of submonoids of the uniform block permutations containing the symmetric group
• Cellular subalgebras of the partition algebra