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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Mots-clés : partition algebra, plethysm, representation theory of semigroups, symmetric functions
@article{ALCO_2022__5_5_1165_0, author = {Orellana, Rosa and Saliola, Franco and Schilling, Anne and Zabrocki, Mike}, title = {Plethysm and the algebra of uniform block permutations}, journal = {Algebraic Combinatorics}, pages = {1165--1203}, publisher = {The Combinatorics Consortium}, volume = {5}, number = {5}, year = {2022}, doi = {10.5802/alco.243}, language = {en}, url = {http://www.numdam.org/articles/10.5802/alco.243/} }
TY - JOUR AU - Orellana, Rosa AU - Saliola, Franco AU - Schilling, Anne AU - Zabrocki, Mike TI - Plethysm and the algebra of uniform block permutations JO - Algebraic Combinatorics PY - 2022 SP - 1165 EP - 1203 VL - 5 IS - 5 PB - The Combinatorics Consortium UR - http://www.numdam.org/articles/10.5802/alco.243/ DO - 10.5802/alco.243 LA - en ID - ALCO_2022__5_5_1165_0 ER -
%0 Journal Article %A Orellana, Rosa %A Saliola, Franco %A Schilling, Anne %A Zabrocki, Mike %T Plethysm and the algebra of uniform block permutations %J Algebraic Combinatorics %D 2022 %P 1165-1203 %V 5 %N 5 %I The Combinatorics Consortium %U http://www.numdam.org/articles/10.5802/alco.243/ %R 10.5802/alco.243 %G en %F ALCO_2022__5_5_1165_0
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. http://www.numdam.org/articles/10.5802/alco.243/
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