Consequences of the Lakshmibai-Sandhya Theorem: the ubiquity of permutation patterns in Schubert calculus and related geometry

zbMath1378.14053arXiv1403.4345MaRDI QIDQ4590914

Sara C. Billey, Hiraku Abe

Publication date: 20 November 2017

Full work available at URL: https://arxiv.org/abs/1403.4345

zbMATH Keywords

Coxeter groupsSchubert varietiesflag manifoldsBruhat orderpattern avoidanceKazhdan-Lustig polynomials

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Grassmannians, Schubert varieties, flag manifolds (14M15) Classical problems, Schubert calculus (14N15)

Related Items (16)

On pattern avoidance in matchings and involutions ⋮ Geometry of Hessenberg varieties with applications to Newton-Okounkov bodies ⋮ Combinatorics of diagrams of permutations ⋮ Diagonal degenerations of matrix Schubert varieties ⋮ Classification of Levi-spherical Schubert varieties ⋮ Positivity of permutation pattern character polynomials ⋮ A tightness property of relatively smooth permutations ⋮ Singularities of Schubert varieties within a right cell ⋮ Pattern avoidance and fiber bundle structures on Schubert varieties ⋮ Pattern avoidance and fiber bundle structures on Schubert varieties ⋮ Transition formulas for involution Schubert polynomials ⋮ Some combinatorial results on smooth permutations ⋮ Stable characters from permutation patterns ⋮ Permutation patterns and cell decompositions ⋮ \(\mathsf{K}\)-orbit closures and Barbasch-Evens-Magyar varieties ⋮ Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras

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