Newell–Littlewood numbers II: extended Horn inequalities

Abstract

The Newell–Littlewood numbers N μ,ν,λ are tensor product multiplicities of Weyl modules for classical Lie groups, in the stable limit. For which triples of partitions (μ,ν,λ) does N μ,ν,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.