Gradient flows, adjoint orbits, and the topology of totally nonnegative flag varieties

DOI10.1007/s00220-022-04540-5OpenAlexW4313378568MaRDI QIDQ2692767

Steven N. Karp, Anthony M. Bloch

Publication date: 23 March 2023

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

Full work available at URL: https://arxiv.org/abs/2109.04558

Mathematics Subject Classification ID

Basic linear algebra (15Axx) Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems (37Kxx) Special varieties (14Mxx)

Related Items

Symmetric Toda, gradient flows, and tridiagonalization, On two notions of total positivity for partial flag varieties

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Total positivity criteria for partial flag varieties
• Sign variation, the Grassmannian, and total positivity
• A convexity theorem for isospectral manifolds of Jacobi matrices in a compact Lie algebra
• The topology of isospectral manifolds of tridiagonal matrices
• On totally positive matrices
• Hamiltonian group actions and integrable systems
• The QR algorithm and scattering for the finite nonperiodic Toda lattice
• Totally positive matrices and cyclic polytopes
• Poisson Lie groups, dressing transformations, and Bruhat decompositions
• The solution to a generalized Toda lattice and representation theory
• Manifolds, tensor analysis, and applications.
• Completely integrable gradient flows
• An algebraic cell decomposition of the nonnegative part of a flag variety
• Hamiltonian and gradient structures in the Toda flows
• Group actions and deformations for harmonic maps
• Completeness of real Toda flows and totally positive matrices
• Toda flows and real Hessenberg manifolds
• Total positivity and Toda flow
• The amplituhedron and the one-loop Grassmannian measure
• Positive geometries and canonical forms
• Some more amplituhedra are contractible
• Unwinding the amplituhedron in binary
• Parametrizations of canonical bases and totally positive matrices
• The amplituhedron
• The totally nonnegative part of \(G/P\) is a ball
• Regularity theorem for totally nonnegative flag varieties
• The full Kostant-Toda hierarchy on the positive flag variety
• Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians
• Bruhat order in full symmetric Toda system
• Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems
• On two notions of total positivity for partial flag varieties
• Grassmannian Geometry of Scattering Amplitudes
• Matrices with totally positive powers and their generalizations
• Combinatorics of Coxeter Groups
• Ordinary Differential Equations and the Symmetric Eigenvalue Problem
• Total Positivity, $QR$ Factorization, and Neville Elimination
• Neighborhoods of Algebraic Sets
• The toda flow on a generic orbit is integrable
• Convexity and Commuting Hamiltonians
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
• Double Bruhat cells and total positivity
• The infinitesimal cone of a totally positive semigroup
• The Toda lattice. II. Existence of integrals
• Fifty years of the finite nonperiodic Toda lattice: a geometric and topological viewpoint
• Spaces of Lorentzian and real stable polynomials are Euclidean balls
• Parity duality for the amplituhedron
• Moment curves and cyclic symmetry for positive Grassmannians
• The $m=1$ Amplituhedron and Cyclic Hyperplane Arrangements
• Gradient Flows in the Normal and Kähler Metrics and Triple Bracket Generated Metriplectic Systems
• Shelling totally nonnegative flag varieties
• Integrals of nonlinear equations of evolution and solitary waves
• Totally nonnegative Grassmannian and Grassmann polytopes
• Lie groups beyond an introduction
• The totally nonnegative Grassmannian is a ball
• Total positivity: tests and parametrizations.
• Dressing transformations and Poisson group actions
• Nonlinear wave equations and constrained harmonic motion