The full Kostant-Toda hierarchy on the positive flag variety

DOI10.1007/s00220-014-2203-xzbMath1319.37048arXiv1308.5011OpenAlexW3100683879MaRDI QIDQ2260714

Yuji Kodama, Lauren K. Williams

Publication date: 11 March 2015

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.5011

zbMATH Keywords

flag varietyGrassmannianmoment polytopeKostant-Toda lattice

Mathematics Subject Classification ID

Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Grassmannians, Schubert varieties, flag manifolds (14M15) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20)

Related Items (21)

Bruhat order in the full symmetric \(\mathfrak{sl}_n\) Toda lattice on partial flag space ⋮ Hessenberg varieties, Slodowy slices, and integrable systems ⋮ The generalized lifting property of Bruhat intervals ⋮ Bruhat interval polytopes ⋮ Generalizations of the finite nonperiodic Toda lattice and its Darboux transformation ⋮ Extended Schur's \(Q\)-functions and the full Kostant-Toda hierarchy on the Lie algebra of type \(D\) ⋮ Symmetric Toda, gradient flows, and tridiagonalization ⋮ Complexity of the usual torus action on Kazhdan-Lusztig varieties ⋮ Subdivisions of generalized permutahedra ⋮ A pattern avoidance characterization for smoothness of positroid varieties ⋮ Positive tropical flags and the positive tropical Dressian ⋮ Lusztig factorization dynamics of the full Kostant-Toda lattices ⋮ KP solitons and the Riemann theta functions ⋮ One-skeleton posets of Bruhat interval polytopes ⋮ On two notions of total positivity for partial flag varieties ⋮ Gradient flows, adjoint orbits, and the topology of totally nonnegative flag varieties ⋮ Phase portraits of the full symmetric Toda systems on rank-2 groups ⋮ Lattice Points in the Newton Polytopes of Key Polynomials ⋮ Vertices of Schubitopes ⋮ Fifty years of the finite nonperiodic Toda lattice: a geometric and topological viewpoint ⋮ Toric Richardson varieties of Catalan type and Wedderburn-Etherington numbers

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