  The Newell-Littlewood numbers are defined in terms of their celebrated
cousins, the Littlewood-Richardson coefficients. Both arise as tensor product
multiplicities for a classical Lie group. They are the structure coefficients
of the K. Koike-I. Terada basis of the ring of symmetric functions. Recent work
of H. Hahn studies them, motivated by R. Langlands' beyond endoscopy proposal;
we address her work with a simple characterization of detection of Weyl
modules. This motivates further study of the combinatorics of the numbers. We
consider analogues of ideas of J. De Loera-T. McAllister, H. Derksen-J. Weyman,
S. Fomin-W. Fulton-C.-K. Li-Y.-T. Poon, W. Fulton, R. King-C. Tollu-F.
Toumazet, M. Kleber, A. Klyachko, A. Knutson-T. Tao, T. Lam-A. Postnikov-P.
Pylyavskyy, K. Mulmuley-H. Narayanan-M. Sohoni, H. Narayanan, A. Okounkov, J.
Stembridge, and H. Weyl.
