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Plethysm and the algebra of uniform block permutations
2022
Algebraic Combinatorics
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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.
doi:10.5802/alco.243
fatcat:k363fzmon5c77e5xtea6fbmbyq