Geodesic
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, Tome 5 (2022) no. 5, pp. 1165-1203 Cet article a éte moissonné depuis la source Numdam

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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.

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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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Plethysm and the algebra of uniform block permutations},
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     pages = {1165--1203},
     year = {2022},
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Orellana, Rosa; Saliola, Franco; Schilling, Anne; Zabrocki, Mike. Plethysm and the algebra of uniform block permutations. Algebraic Combinatorics, Tome 5 (2022) no. 5, pp. 1165-1203. doi: 10.5802/alco.243

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