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Factorization of Kazhdan-Lusztig elements for Grassmannians. (English) Zbl 1002.20004

Koike, Kazuhiko (ed.) et al., Combinatorial methods in representation theory. Papers of the conference on combinatorial methods in representation theory, July 21-July 31, 1998 and the conference on interaction of combinatorics and representation theory, October 26-November 6, 1998, Kyoto, Japan. Tokyo: Kinokuniya Company Ltd. Adv. Stud. Pure Math. 28, 143-154 (2000).
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.
For the entire collection see [Zbl 0963.00024].

MSC:

20C08 Hecke algebras and their representations
14M15 Grassmannians, Schubert varieties, flag manifolds
20C30 Representations of finite symmetric groups
05E10 Combinatorial aspects of representation theory
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