ALGEBRAIC COMBINATORICS

no. 5
Plethysm and the algebra of uniform block permutations
Orellana, Rosa1; Saliola, Franco2; Schilling, Anne3; Zabrocki, Mike4
1 Mathematics Department Dartmouth College Hanover NH 03755 U.S.A.
2 Département de mathématiques, Université du Québec à Montréal, Canada
3 Department of Mathematics, University of California, One Shields Avenue, Davis, CA 95616-8633, U.S.A.
4 Department of Mathematics and Statistics York University 4700 Keele Street Toronto Ontario M3J 1P3 Canada
Algebraic Combinatorics, Volume 5 (2022) no. 5, pp. 1165-1203.

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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.243
Classification: 05E10, 05E05, 20M30
Keywords: partition algebra, plethysm, representation theory of semigroups, symmetric functions
Orellana, Rosa 1; Saliola, Franco 2; Schilling, Anne 3; Zabrocki, Mike 4

1 Mathematics Department Dartmouth College Hanover NH 03755 U.S.A.
2 Département de mathématiques, Université du Québec à Montréal, Canada
3 Department of Mathematics, University of California, One Shields Avenue, Davis, CA 95616-8633, U.S.A.
4 Department of Mathematics and Statistics York University 4700 Keele Street Toronto Ontario M3J 1P3 Canada
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Orellana, Rosa; Saliola, Franco; Schilling, Anne; Zabrocki, Mike. Plethysm and the algebra of uniform block permutations. Algebraic Combinatorics, Volume 5 (2022) no. 5, pp. 1165-1203. doi : 10.5802/alco.243. https://alco.centre-mersenne.org/articles/10.5802/alco.243/

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