Factorization of Kazhdan-Lusztig elements for Grassmannians (Q2741034)
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scientific article; zbMATH DE number 1642287
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Factorization of Kazhdan-Lusztig elements for Grassmannians |
scientific article; zbMATH DE number 1642287 |
Statements
9 October 2002
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Kazhdan-Lusztig polynomials
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Young diagrams
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Hecke algebras
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Kazdan-Lusztig bases
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0.8909306
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0.89053833
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0.88965607
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0.88554794
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0.88268054
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0.88116693
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Factorization of Kazhdan-Lusztig elements for Grassmannians (English)
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Given a symmetric group and a maximal parabolic subgroup, minimal length coset representatives can be indexed by Young diagrams fitting inside a rectangle. It is shown that parabolic Kazhdan-Lusztig basis elements in the corresponding Hecke algebra can be written as a product of factors which are differences between a standard generator and a rational function in \(v\). The factors depend in a combinatorial way on the Young diagram corresponding to the index of the basis element. A factorization for the dual Kazhdan-Lusztig basis is also obtained.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00024].
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