Self-dual intervals in the Bruhat order

DOI10.1007/s00029-020-00608-zzbMath1455.05079arXiv2003.06710OpenAlexW3103491426MaRDI QIDQ2218155

Christian Gaetz, Yibo Gao

Publication date: 14 January 2021

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.06710

zbMATH Keywords

Weyl groupSchubert varietyintersection cohomologyBruhat orderKazhdan-Lusztig polynomial

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43) Classical problems, Schubert calculus (14N15) Combinatorial aspects of algebraic geometry (05E14)

Related Items (2)

On automorphisms of undirected Bruhat graphs ⋮ Poincaré Polynomials of Odd Diagram Classes

Cites Work

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• Billey-Postnikov decompositions and the fibre bundle structure of Schubert varieties
• On the shape of Bruhat intervals
• Criterion for smoothness of Schubert varieties in Sl(n)/B
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• Bruhat order, smooth Schubert varieties, and hyperplane arrangements
• Bruhat order of Coxeter groups and shellability
• Factoring the Poincaré polynomials for the Bruhat order on \(S_n\)
• The parabolic map
• Pattern avoidance and the Bruhat order.
• Staircase diagrams and enumeration of smooth Schubert varieties
• Rationally smooth elements of Coxeter groups and triangle group avoidance.
• Smoothness of Schubert varieties via patterns in root subsystems
• Combinatorics of Coxeter Groups
• Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property

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