The biflag manifold and the fixed points of a unipotent transformation on the flag manifold

DOI10.1016/0024-3795(87)90254-0zbMath0646.57012OpenAlexW2075139414MaRDI QIDQ1103920

Mark A. Shayman, Uwe R. Helmke

Publication date: 1987

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(87)90254-0

zbMATH Keywords

flag manifoldBetti numbersstrong deformation retractbiflag manifoldcompact nonsingular projective variety

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Basic linear algebra (15A99) Homology and cohomology of homogeneous spaces of Lie groups (57T15) Algebraic topology on manifolds and differential topology (57R19)

Related Items (4)

Generalized Eulerian numbers and the topology of the Hessenberg variety of a matrix ⋮ Versal deformations in generalized flag manifolds ⋮ The topology of the set of conditioned invariant subspaces ⋮ A cellular decomposition of the manifold of observable conditioned invariant subspaces

Cites Work

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• The fixed point subvarieties of unipotent transformations on the flag varieties
• The geometry of matrix eigenvalue methods
• The fixed point subvarieties of unipotent transformations on generalized flag varieties and the Green functions. Combinatorial and cohomological treatments centering \(GL_ n\).
• Classes unipotentes et sous-groupes de Borel
• On the desingularization of the unipotent variety
• A construction of representations of Weyl groups
• A theorem on the fixed point set of a unipotent transformation of the flag manifold
• On a topology for invariant subspaces
• Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts
• On the Variety of Invariant Subspaces of a Finite-Dimensional Linear Operator
• On Related Periodic Maps

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