On the quantum Horn problem

2013/10/28 by Nicolas Ressayre, Ressayre, Nicolas · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.1310.7331

Belkale-Kumar obtained independently the results of this paper in arXiv:1310.3191

arxiv created 2013/10/28 · arxiv updated 2013/10/29

Abstract

Let K be a compact, connected, simply-connected simple Lie group. Given two conjugacy classes \Orb₁ and \Orb₂ in K, we consider the multiplicative Horn question: What conjugacy classes are contained in \Orb₁⋅\Orb₂? It is known that answering this question remains to describe a convex polytope \poly_K. In 2003, Teleman-Woodward gave a complete list of inequalities for \poly_K. Their list contains redundant inequalities. In this paper, we describe \poly_K by a smaller list of inequalities.

Citations

• The multiplicative eigenvalue problem and deformed quantum cohomology

Cited by

• Horn's problem in PU(n,1)
• The multiplicative eigenvalue problem and deformed quantum cohomology

Related

• Horn's problem in PU(n,1)
• Vertices in multiplicative eigenvalue problem for arbitrary groups
• Positive formula for the product of conjugacy classes on the unitary group
• Connes-Landi spheres are homogeneous spaces
• Geometric Complexity Theory VII: Nonstandard quantum group for the plethysm problem