Polynomial representations of the Hecke algebra of the symmetric group. (Q2842021)
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scientific article; zbMATH DE number 6192875
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Polynomial representations of the Hecke algebra of the symmetric group. |
scientific article; zbMATH DE number 6192875 |
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30 July 2013
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Young bases
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polynomial bases
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irreducible representations
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Hecke algebras
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symmetric groups
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Jucys-Murphy elements
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0.9293932
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0.9287534
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0.9260665
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0.9200363
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0.9189972
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0.91624177
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Polynomial representations of the Hecke algebra of the symmetric group. (English)
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In the article under review, the author uses a generalization of the Yang-Baxter graph for the irreducible representations of the symmetric group to construct a polynomial basis (and an adjoint basis) for each irreducible representation of the Hecke algebra of the symmetric group. This basis satisfies easy vanishing properties, and decompositions can be obtained by specializations. In addition, each polynomial in the basis is a simultaneous eigenfunction of the Jucys-Murphy elements.
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