Newell-Littlewood numbers II: extended Horn inequalities

Abstract

The Newell-Littlewood numbers $N_{\mu ,\nu ,\lambda }$ are tensor product multiplicities of Weyl modules for classical Lie groups, in the stable limit. For which triples of partitions $(\mu ,\nu ,\lambda )$ does $N_{\mu ,\nu ,\lambda }>0$ 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.

11 pages. To appear in Algebraic Combinatorics

References in corpus (1)

• Newell-Littlewood numbers

Cited by in corpus (1)

• Newell-Littlewood numbers III: eigencones and GIT-semigroups