Journal of Symplectic Geometry
Volume 15 (2017)
Inequalities for moment cones of finite-dimensional representations
Pages: 1209 – 1250
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.
Paper received on 14 April 2015.
Paper accepted on 27 January 2016.