Plethysm and the algebra of uniform block permutations

Rosa Orellana, Franco Saliola, Anne Schilling, Mike Zabrocki
2022 Algebraic Combinatorics  
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