Combinatorial invariance of Kazhdan-Lusztig polynomials on intervals starting from the identity

被引：0

作者：

Ewan Delanoy

机构：

[1] Université Lyon 1,Institut Camille Jordan, UMR 5208 CNRS

来源：

Journal of Algebraic Combinatorics | 2006年 / 24卷

关键词：

Coxeter group; Kazhdan-Lusztig polynomials; Special matching;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We show that for Bruhat intervals starting from the identity in Coxeter groups the conjecture of Lusztig and Dyer holds, that is, the R-polynomials and the Kazhdan-Lusztig polynomials defined on [e,u] only depend on the isomorphism type of [e,u]. To achieve this we use the purely poset-theoretic notion of special matching. Our approach is essentially a synthesis of the explicit formula for special matchings discovered by Brenti and the general special matching machinery developed by Du Cloux.

引用

页码：437 / 463

页数：26

共 8 条

[1] Brenti F.(1994)A combinatorial formula for Kazhdan-Lusztig polynomials Invent. Math. 118 371-394
[2] Brenti F.(2004)The intersection cohomology of Schubert varieties is a combinatorial invariant Europ. J. Combin. 25 1151-1167
[3] du Cloux F.(2000)An abstract model for Bruhat intervals Europ. J. Combin. 21 197-222
[4] du Cloux F.(2003)Rigidity of Schubert closures and invariance of Kazhdan-Lusztig polynomials Adv. in Math. 180 146-175
[5] du Cloux F.(1999)A transducer approach to Coxeter groups J. Symb. Comp 27 1-14
[6] Kazhdan D.(1979)Representations of Coxeter Groups and Hecke Algebras Invent. Math. 53 165-184
[7] Lusztig G.(1989)Automorphisms of the Bruhat ordering on Coxeter groups Bull. London Math. Soc. 21 243-248
[8] Waterhouse W.C.(undefined)undefined undefined undefined undefined-undefined

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