Kazhdan-Lusztig polynomials for certain varieties of incomplete flags

DOI10.1016/S0012-365X(97)00124-6zbMath0915.14029WikidataQ127646326 ScholiaQ127646326MaRDI QIDQ1381836

A. D. Vaĭnshteĭn, Boris Zalmanovich Shapiro, Michael Shapiro

Publication date: 28 June 1999

Published in: Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

symmetric groupCoxeter groupKazhdan-Lusztig polynomialsSchubert cells\(R\)-polynomials\(P\)-polynomialssingularity of a Schubert variety

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Grassmannians, Schubert varieties, flag manifolds (14M15)

Related Items

Kazhdan-Lusztig \(R\)-polynomials of permutations containing a 231 or 312 pattern, Proof of two conjectures of Brenti and Simion on Kazhdan-Lusztig polynomials, On 1234-nesting Kazhdan–Lusztig R-polynomials for the symmetric group, Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations, Formulas for multi-parameter classes of Kazhdan-Lusztig polynomials in \({\mathfrak S}(n)\), Maximal singular loci of Schubert varieties in $SL(n)/B$, Explicit formulae for some Kazhdan-Lusztig polynomials, Kazhdan-Lusztig and \(R\)-polynomials from a combinatorial point of view., Boolean elements in Kazhdan-Lusztig theory.

Cites Work

• Criterion for smoothness of Schubert varieties in Sl(n)/B
• A combinatorial setting for questions in Kazhdan-Lusztig theory
• Small resolutions of singularities of Schubert varieties
• On some generalizations of the Kazhdan-Lusztig polynomials for ``universal Coxeter systems
• Representations of Coxeter groups and Hecke algebras
• Singular locus of a Schubert variety
• A Further Refinement of the Bruhat Decomposition
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