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arXiv · 2112.13909

Plethysm and the algebra of uniform block permutations

Rosa Orellana·Franco Saliola·Anne Schilling·Mike Zabrocki
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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.

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Rosa Orellana, Franco Saliola, Anne Schilling, Mike Zabrocki. 2022-08-24. Plethysm and the algebra of uniform block permutations. https://doi.org/10.5802/alco.243

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