Newell-Littlewood numbers II: extended Horn inequalities

The Newell-Littlewood numbers Nμ,v,λ are tensor product multiplicities of Weyl modules for classical Lie groups, in the stable limit. For which triples of partitions (μ, v, λ) does Nμ,v,λ > 0 hold? The Littlewood-Richardson coefficient case is solved by the Horn inequalities (in work of A. Klyachko and A. Knutson-T. Tao). We extend these celebrated linear inequalities to a much larger family, suggesting a general solution.