Alexander Yong, University of Illinois at Urbana-Champaign

Title: Newell-Littlewood numbers

Abstract: 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, Gidon Orelowitz, and Nicolas Ressayre. The presentation is based on arXiv:2005.09012, arXiv:2009.09904, and arXiv:2107.03152.