Kirillov, Alexander jun.; Lascoux, Alain 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]. Reviewer: Steffen König (Leicester) Cited in 7 Documents 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 Keywords:Kazhdan-Lusztig polynomials; Young diagrams; Hecke algebras; Kazdan-Lusztig bases PDFBibTeX XMLCite \textit{A. Kirillov jun.} and \textit{A. Lascoux}, Adv. Stud. Pure Math. 28, 143--154 (2000; Zbl 1002.20004) Full Text: arXiv