#### IMSc Webinar

#### Newell-Littlewood Numbers

#### Alexander Yong

##### University of Illinois at Urbana-Champaign

*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.

zoom.us/j/91288928049?pwd=WHNaUE9TZEdZWGR3aGNtN2JvWDNtZz09

Done