On Zariski tangent spaces of Schubert varieties, and a proof of a conjecture of Deodhar

DOI10.1016/0019-3577(94)90019-1zbMath0833.20050OpenAlexW1966233353WikidataQ123191813 ScholiaQ123191813MaRDI QIDQ1842551

Patrick Polo

Publication date: 23 January 1996

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0019-3577(94)90019-1

zbMATH Keywords

Schubert varietiesfinite Weyl groupsBruhat intervalsZariski tangent spaces

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Combinatorics of partially ordered sets (06A07) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Grassmannians, Schubert varieties, flag manifolds (14M15)

Related Items (11)

Singularities of Generalized Richardson Varieties ⋮ Equivariant Chow groups for torus actions ⋮ The nil Hecke ring and singularity of Schubert varieties ⋮ On tangent cones of Schubert varieties ⋮ Smooth Schubert varieties in \(G/B\) and \(B\)-submodules of \(\mathfrak{g}/\mathfrak{b}\) ⋮ On tangent spaces to Schubert varieties. II ⋮ Classes d'Euler équivariantes et points rationnellement lisses. (Equivariant Euler classes and rationally smooth points.) ⋮ Casselman’s Basis of Iwahori Vectors and Kazhdan–Lusztig Polynomials ⋮ On tangent spaces to Schubert varieties ⋮ Rational smoothness and fixed points of torus actions ⋮ Smoothness of Schubert varieties indexed by involutions in finite simply laced types

Cites Work

• Projective normality of flag varieties and Schubert varieties
• Schubert varieties and Demazure's character formula
• Geometry of G/P. V
• Geometry of G/P. VI: Bases for fundamental represenations of classical groups. Geometry of G/P. VII: The symplectic group and the involution \(\sigma\) . Geometry of G/P. VIII: The group \(SO(2n+1)\) and the involution \(\sigma\)
• Some characterizations of Bruhat ordering on a Coxeter group and determination of the relation Möbius function
• The nil Hecke ring and Deodhar's conjecture on Bruhat intervals
• Multi-cones over Schubert varieties
• Singular locus of a Schubert variety
• Local poincaré duality and non-singularity of schubert varieties
• Darstellungen halbeinfacher Gruppen und kontravariante Formen.
• SCHUBERT CELLS AND COHOMOLOGY OF THE SPACESG/P
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