Pattern characterization of rationally smooth affine Schubert varieties of type \(A\)

DOI10.1016/j.jalgebra.2012.03.019zbMath1273.14099arXiv1008.5370OpenAlexW2963677778MaRDI QIDQ1931686

Andrew Crites, Sara C. Billey

Publication date: 15 January 2013

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.5370

zbMATH Keywords

pattern avoidanceaffine flag varietiesrational smoothnessSchubert Varieties

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Grassmannians, Schubert varieties, flag manifolds (14M15) Singularities of surfaces or higher-dimensional varieties (14J17)

Related Items (6)

Bounded affine permutations. II: Avoidance of decreasing patterns ⋮ Billey-Postnikov decompositions and the fibre bundle structure of Schubert varieties ⋮ Staircase diagrams and enumeration of smooth Schubert varieties ⋮ The Bruhat order, the lookup conjecture and spiral Schubert varieties of type \(\tilde{A}_2\) ⋮ Bounded affine permutations I. Pattern avoidance and enumeration ⋮ Smooth Schubert varieties in the affine flag variety of type \(\tilde{A}\)

Uses Software

• OEIS

Cites Work

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• On the shape of Bruhat intervals
• Criterion for smoothness of Schubert varieties in Sl(n)/B
• A combinatorial approach to the singularities of Schubert varieties
• Singularities of affine Schubert varieties
• On Schubert varieties in the flag manifold of Sl(n,\({\mathbb C})\)
• The Kazhdan-Lusztig cells in certain affine Weyl groups
• Factoring the Poincaré polynomials for the Bruhat order on \(S_n\)
• The parabolic map
• A filtration of the loops on SU\((N)\) by Schubert varieties
• Subword complexes in Coxeter groups.
• Kac-Moody groups, their flag varieties and representation theory
• Enumerating pattern avoidance for affine permutations
• Schubert polynomials for the affine Grassmannian of the symplectic group
• Affine partitions and affine Grassmannians
• Smoothness of Schubert varieties via patterns in root subsystems
• Combinatorics of Coxeter Groups
• Some Examples of Square Integrable Representations of Semisimple p-Adic Groups
• Affine insertion and Pieri rules for the affine Grassmannian
• Affine Stanley symmetric functions
• Local poincaré duality and non-singularity of schubert varieties
• Maximal singular loci of Schubert varieties in $SL(n)/B$
• Cohomology of Smooth Schubert Varieties in Partial Flag Manifolds
• Lectures on the Geometry of Flag Varieties

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