Flag manifold quantum cohomology, the Toda lattice, and the representation with highest weight \(\rho\)

DOI10.1007/BF01587939zbMath0868.14024MaRDI QIDQ1919131

Bertram Kostant

Publication date: 20 October 1996

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

zbMATH Keywords

flag manifoldaffine algebras

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Applications of linear algebraic groups to the sciences (20G45)

Related Items

Totally positive Toeplitz matrices and quantum cohomology of partial flag varieties ⋮ The equivariant cohomology ring of regular varieties ⋮ Total positivity, Schubert positivity, and geometric Satake ⋮ Hessenberg varieties, Slodowy slices, and integrable systems ⋮ Intersection theory of the Peterson variety and certain singularities of Schubert varieties ⋮ Quantum cohomology rings of Lagrangian and orthogonal Grassmannians and total positivity ⋮ Geometry of Hessenberg varieties with applications to Newton-Okounkov bodies ⋮ Kostant-Toda lattices and the universal centralizer ⋮ Normal forms for orthogonal similarity classes of skew-symmetric matrices ⋮ Geometry of regular Hessenberg varieties ⋮ On the convergence of Gromov-Witten potentials and Givental's formula ⋮ A positive formula for type a Peterson Schubert calculus ⋮ Quantum cohomology of \(G/P\) and homology of affine Grassmannian ⋮ The partial compactification of the universal centralizer ⋮ Patch ideals and Peterson varieties ⋮ The Peterson variety and the wonderful compactification ⋮ The cohomology rings of regular nilpotent Hessenberg varieties and Schubert polynomials ⋮ Critical varieties in the Grassmannian ⋮ Generalizing Tanisaki's ideal via ideals of truncated symmetric functions ⋮ An additive basis for the cohomology rings of regular nilpotent Hessenberg varieties ⋮ Floer cohomology of -equivariant Lagrangian branes ⋮ Toward cohomology rings of intersections of Peterson varieties and Richardson varieties ⋮ Poset pinball, the dimension pair algorithm, and type \(A\) regular nilpotent Hessenberg varieties ⋮ A Survey of Recent Developments on Hessenberg Varieties ⋮ A mirror symmetric solution to the quantum Toda lattice ⋮ Hessenberg varieties of parabolic type ⋮ The geometry and combinatorics of Springer fibers ⋮ The equivariant cohomology rings of Peterson varieties ⋮ Clifford algebra analogue of the Hopf-Koszul-Samelson theorem, the \(\rho\)-decomposition \(C({\mathfrak g})=\text{End }V_ \rho\otimes C(P)\), and the \({\mathfrak g}\)-module structure of \(\bigwedge {\mathfrak g}\) ⋮ The singular locus of semisimple Hessenberg varieties ⋮ A mirror symmetric construction of \(qH_T^*(G/P)_{(q)}\) ⋮ Large values of cusp forms on \(\mathrm{GL}_n\) ⋮ Monk's rule and Giambelli's formula for Peterson varieties of all Lie types ⋮ Schubert polynomials and classes of Hessenberg varieties ⋮ On the spectral resolution of the quantum Toda lattice ⋮ Exponents for 𝐵-stable ideals ⋮ A formula for the cohomology and \(K\)-class of a regular Hessenberg variety ⋮ A Mirror Construction for the Totally Nonnegative Part of the Peterson Variety ⋮ \(k\)-Schur expansions of Catalan functions ⋮ Quantum cohomology rings of Grassmannians and total positivity ⋮ The Cohomology Rings of Regular Nilpotent Hessenberg Varieties in Lie Type A ⋮ Schubert calculus and the homology of the Peterson variety

Cites Work

• Unnamed Item
• The nil Hecke ring and cohomology of \(G/P\) for a Kac-Moody group \(G\)
• The solution to a generalized Toda lattice and representation theory
• On Whittaker vectors and representation theory
• Quantum cohomology of flag manifolds and Toda lattices
• Lie algebra cohomology and the generalized Borel-Weil theorem
• Lie algebra cohomology and generalized Schubert cells
• Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• A simple proof of Kostant's theorem that U(g) is free over its center
• SCHUBERT CELLS AND COHOMOLOGY OF THE SPACESG/P
• Quantum cohomology of flag varieties
• Lie Group Representations on Polynomial Rings
• A mathematical theory of quantum cohomology