Generalized Eulerian numbers and the topology of the Hessenberg variety of a matrix

DOI10.1007/BF00046881zbMath0661.65041MaRDI QIDQ1113614

Filippo de Mari, Mark A. Shayman

Publication date: 1988

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

zbMATH Keywords

eigenvaluesEulerian numbersBetti numbersHessenberg formHessenberg varietyQR-iteration

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Factorials, binomial coefficients, combinatorial functions (05A10) Grassmannians, Schubert varieties, flag manifolds (14M15) Homogeneous complex manifolds (32M10)

Related Items (20)

Chromatic quasisymmetric functions ⋮ Hessenberg varieties, Slodowy slices, and integrable systems ⋮ Geometry of Hessenberg varieties with applications to Newton-Okounkov bodies ⋮ Rigid two-step nilpotent Lie groups relative to multicontact structures ⋮ Geometry of regular Hessenberg varieties ⋮ Bases of the equivariant cohomologies of regular semisimple Hessenberg varieties ⋮ The cohomology rings of regular nilpotent Hessenberg varieties and Schubert polynomials ⋮ An additive basis for the cohomology rings of regular nilpotent Hessenberg varieties ⋮ Fano and weak Fano Hessenberg varieties ⋮ A Survey of Recent Developments on Hessenberg Varieties ⋮ Hessenberg varieties of parabolic type ⋮ Some applications of algebra to combinatorics ⋮ Reduction to generalized Hessenberg form and inverse spectral problems ⋮ Generic torus orbit closures in Schubert varieties ⋮ A filtration on the cohomology rings of regular nilpotent Hessenberg varieties ⋮ A formula for the cohomology and \(K\)-class of a regular Hessenberg variety ⋮ Hessenberg varieties and hyperplane arrangements ⋮ The Cohomology Rings of Regular Nilpotent Hessenberg Varieties in Lie Type A ⋮ Toda flows and real Hessenberg manifolds ⋮ Descent identities, Hessenberg varieties, and the Weil conjectures

Cites Work

• Eulerian numbers and polynomials of higher order
• Matrix computations.
• The fixed point subvarieties of unipotent transformations on the flag varieties
• The geometry of matrix eigenvalue methods
• The biflag manifold and the fixed points of a unipotent transformation on the flag manifold
• Generalized Toda flows, Riccati equations on the Grassmanian, and the QR- algorithm
• The fixed point subvarieties of unipotent transformations on generalized flag varieties and the Green functions. Combinatorial and cohomological treatments centering \(GL_ n\).
• The r-major index
• Generalized Eulerian numbers
• On the desingularization of the unipotent variety
• A construction of representations of Weyl groups
• Some theorems on actions of algebraic groups
• Eulerian numbers of higher order
• Phase Portrait of the Matrix Riccati Equation
• Homology of the Zero-Set of a Nilpotent Vector Field on a Flag Manifold
• Differentiable dynamical systems
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