The intersection cohomology of Schubert varieties is a combinatorial invariant

DOI10.1016/j.ejc.2003.10.011zbMath1064.14062OpenAlexW2038984633MaRDI QIDQ1888291

Francesco Brenti

Publication date: 23 November 2004

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ejc.2003.10.011

zbMATH Keywords

posetsKazhdan-Lusztig polynomialsBruhat order

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Grassmannians, Schubert varieties, flag manifolds (14M15) Classical problems, Schubert calculus (14N15)

Related Items (20)

Topology of posets with special partial matchings ⋮ The size of Bruhat intervals between nested involutions in \(S_{n}\) ⋮ Special matchings and permutations in Bruhat orders. ⋮ Kazhdan-Lusztig polynomials for maximally-clustered hexagon-avoiding permutations. ⋮ Combinatorial invariance of Kazhdan-Lusztig-Vogan polynomials for fixed point free involutions ⋮ An effective decomposition theorem for Schubert varieties ⋮ On automorphisms of undirected Bruhat graphs ⋮ A simple characterization of special matchings in lower Bruhat intervals ⋮ Completely compressible Bruhat intervals and Kazhdan-Lusztig polynomials ⋮ Combinatorial invariance of Kazhdan-Lusztig polynomials on intervals starting from the identity. ⋮ Rigidity of Schubert closures and invariance of Kazhdan-Lusztig polynomials. ⋮ Algebraic and combinatorial properties of zircons ⋮ Fixed points of zircon automorphisms ⋮ Equivalence Classes for the μ-Coefficient of Kazhdan–Lusztig Polynomials inS_n ⋮ Special matchings and Kazhdan-Lusztig polynomials ⋮ Special matchings in Coxeter groups ⋮ Special idempotents and projections ⋮ Topology of posets with special partial matchings ⋮ Casselman’s Basis of Iwahori Vectors and Kazhdan–Lusztig Polynomials ⋮ Towards combinatorial invariance for Kazhdan-Lusztig polynomials

Cites Work

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• Ordering the symmetric group: why using the Iwahori-Hecke algebra?
• Representations of Coxeter groups and Hecke algebras
• A combinatorial formula for Kazhdan-Lusztig polynomials
• Rigidity of Schubert closures and invariance of Kazhdan-Lusztig polynomials.
• Singular loci of Schubert varieties
• Kazhdan-Lusztig and \(R\)-polynomials from a combinatorial point of view.
• An abstract model for Bruhat intervals
• Subdivisions and Local h-Vectors
• Algebraic groups and modular Lie algebras

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