The Newell-Littlewood numbers are defined in terms of the Littlewood-Richardson coefficients from algebraic combinatorics. Both appear in representation theory as tensor product multiplicities for a classical Lie group. This talk concerns the question, Which multiplicities are nonzero?
In 1998, Klyachko established common linear inequalities defining both the eigencone for sums of Hermitian matrices and the saturated Littlewood-Richardson cone. We prove some analogues of Klyachko's nonvanishing results for the Newell-Littlewood numbers.
This is joint work with Shiliang Gao (UIUC), Gidon Orelowitz (UIUC), and Nicolas Ressayre (Universite Claude Bernard Lyon I). The presentation is based on arXiv:2005.09012, arXiv:2009.09904, and arXiv:2107.03152.
