Moment polytopes in real symplectic geometry II : applications to\n singular value inequalities

2021/11/26 by Paul-Émile Paradan, Paradan, Paul-Emile
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Representation Theory (math.RT) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2111.13399

openalex publication_date 2021/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we study some convex cones associated to isotropic\nrepresentations of symmetric spaces. We explain the inequalities that describe\nthem by means of cohomological conditions. In particular, we study the singular\nHorn cone which is the counterpart of the classical Horn cone, where the\neigenvalues of Hermitian square matrices are replaced by the singular values of\nrectangular matrices.\n

Citations

• Moment polytopes in real symplectic geometry I

Related

• The Horn cone associated with symplectic eigenvalues
• Moment maps and Riemannian symmetric pairs
• A symplectic proof of the Horn inequalities
• Moment polytopes for symplectic manifolds with monodromy
• Moment maps and Isoparametric hypersurfaces in spheres --- Hermitian cases