Newell-littlewood numbers

Shiliang Gao, Gidon Orelowitz, Alexander Yong

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)6331-6366
Number of pages36
JournalTransactions of the American Mathematical Society
Issue number9
StatePublished - 2021

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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