Schubert calculus of a Coxeter group

zbMath0492.57015MaRDI QIDQ1167969

Howard L. Hiller

Publication date: 1981

Published in: L'Enseignement Mathématique. 2e Série (Search for Journal in Brave)

zbMATH Keywords

invariantsSchubert calculusGrassmanniansroot systemfinite Coxeter systemcohomology ring of a flag manifoldgeometry of Coxeter groupsGiambellis formulaPieris formula

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Grassmannians, Schubert varieties, flag manifolds (14M15) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Homogeneous complex manifolds (32M10) Homology and cohomology of homogeneous spaces of Lie groups (57T15)

Related Items (11)

Pieri formula for \(SO_{2n+1}/U_ n\) and \(Sp_ n/U_ n\) ⋮ Noncommutative algebras related with Schubert calculus on Coxeter groups ⋮ Nichols-Woronowicz model of coinvariant algebra of complex reflection groups. ⋮ Strong Lefschetz elements of the coinvariant rings of finite Coxeter groups ⋮ Cohomology of GKM fiber bundles ⋮ Schubert polynomials, the Bruhat order, and the geometry of flag manifolds ⋮ The strong Lefschetz property of the coinvariant ring of the Coxeter group of type \(H_{4}\) ⋮ Power sum decompositions of defining equations of reflection arrangements ⋮ Equivariant cohomology of real flag manifolds ⋮ The strong Lefschetz property for coinvariant rings of finite reflection groups ⋮ A finiteness property and an automatic structure for Coxeter groups

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