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Newell-Littlewood numbers III: eigencones and GIT-semigroups (2107.03152v2)
Published 7 Jul 2021 in math.AG, math.CO, and math.RT
Abstract: The Newell-Littlewood numbers are tensor product multiplicities of Weyl modules for the classical groups in the stable range. Littlewood-Richardson coefficients form a special case. Klyachko connected eigenvalues of sums of Hermitian matrices to the saturated LR-cone and established defining linear inequalities. We prove analogues for the saturated NL-cone: an eigenvalue interpretation; a minimal list of defining linear inequalities; a description by Extended Horn inequalities, as conjectured in part II of this series; and a factorization of NL-numbers, on the boundary.