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The poset of Specht ideals for hyperoctahedral groups

Permanent link
https://hdl.handle.net/10037/31685
DOI
https://doi.org/10.48550/arXiv.2206.08925
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Date
2023
Type
Journal article
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Author
Debus, Sebastian; Moustrou, Philippe; Riener, Cordian Benedikt; Verdure, Hugues
Abstract
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 Bn. We introduce a bidominance order on bipartitions which describes the poset of inclusions of these ideals and study algebraic consequences on general Bn-invariant ideals and varieties, which can lead to computational simplifications.
Citation
Debus, Moustrou, Riener, Verdure. The poset of Specht ideals for hyperoctahedral groups. Algebraic combinatorics. 2023
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