Geodesic
The poset of Specht ideals for hyperoctahedral groups
Debus, Sebastian1 ; Moustrou, Philippe2 ; Riener, Cordian3 ; Verdure, Hugues3
1 Technische Universität Chemnitz Fakultät für Mathematik 09107 Chemnitz (Germany)
2 Université Toulouse Jean Jaures Institut de Mathématiques de Toulouse UMR 5219, UT2J, 31058 Toulouse (France)
3 UiT - the Arctic University of Norway Department of Mathematics and Statistics 9037 Tromsø  (Norway)
Algebraic Combinatorics, Tome 6 (2023) no. 6, pp. 1593-1619

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Specht polynomials classically realize the irreducible representations of the symmetric group. The ideals defined by these polynomials provide a strong connection with the combinatorics of Young tableaux and have been intensively studied by several authors. We initiate similar investigations for the ideals defined by the Specht polynomials associated to the hyperoctahedral group B n . We introduce a bidominance order on bipartitions which describes the poset of inclusions of these ideals and study algebraic consequences on general B n -invariant ideals and varieties, which can lead to computational simplifications.

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DOI : 10.5802/alco.316
Classification : 10X99, 14A12, 11L05
Keywords: bipartitions, Specht polynomials, hyperoctahedral group, invariant ideals

Debus, Sebastian 1 ; Moustrou, Philippe 2 ; Riener, Cordian 3 ; Verdure, Hugues 3

1 Technische Universität Chemnitz Fakultät für Mathematik 09107 Chemnitz (Germany)
2 Université Toulouse Jean Jaures Institut de Mathématiques de Toulouse UMR 5219, UT2J, 31058 Toulouse (France)
3 UiT - the Arctic University of Norway Department of Mathematics and Statistics 9037 Tromsø  (Norway)
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {The poset of {Specht} ideals for hyperoctahedral groups},
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     pages = {1593--1619},
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Debus, Sebastian; Moustrou, Philippe; Riener, Cordian; Verdure, Hugues. The poset of Specht ideals for hyperoctahedral groups. Algebraic Combinatorics, Tome 6 (2023) no. 6, pp. 1593-1619. doi: 10.5802/alco.316

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