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arXiv · 1410.8144

Inequalities for Moment Cones of Finite-Dimensional Representations

Michèle Vergne·Michael Walter
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Abstract

We give a general description of the moment cone associated with an arbitrary finite-dimensional unitary representation of a compact, connected Lie group in terms of finitely many linear inequalities. Our method is based on combining differential-geometric arguments with a variant of Ressayre's notion of a dominant pair. As applications, we obtain generalizations of Horn's inequalities to arbitrary representations, new inequalities for the one-body quantum marginal problem in physics, which concerns the asymptotic support of the Kronecker coefficients of the symmetric group, and a geometric interpretation of the Howe-Lee-Tan-Willenbring invariants for the tensor product algebra.

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Michèle Vergne, Michael Walter. 2014-10-29. Inequalities for Moment Cones of Finite-Dimensional Representations. https://doi.org/10.4310/jsg.2017.v15.n4.a8

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