Newell-Littlewood numbers. II: extended Horn inequalities. (English) Zbl 1504.05298
Summary: 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. A. Klyachko [Sel. Math., New Ser. 4, No. 3, 419–445 (1998; Zbl 0915.14010)] and A. Knutson and T. Tao [J. Am. Math. Soc. 12, No. 4, 1055–1090 (1999; Zbl 0944.05097)]). We extend these celebrated linear inequalities to a much larger family, suggesting a general solution.
For Part I, see [ibid. 374, No. 9, 6331–6366 (2021; Zbl 1536.05471)].
For Part I, see [ibid. 374, No. 9, 6331–6366 (2021; Zbl 1536.05471)].
MSC:
| 05E10 | Combinatorial aspects of representation theory |
| 22E46 | Semisimple Lie groups and their representations |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
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