TY - JOUR
T1 - Newell-littlewood numbers
AU - Gao, Shiliang
AU - Orelowitz, Gidon
AU - Yong, Alexander
N1 - Funding Information:
The third author was partially supported by a Simons Collaboration grant and funding from UIUC's Campus Research Board. This work was also partially supported by NSF RTG 1937241.
Funding Information:
Received by the editors June 14, 2020, and, in revised form, December 3, 2020. 2020 Mathematics Subject Classification. Primary 05E10. The third author was partially supported by a Simons Collaboration grant and funding from UIUC’s Campus Research Board. This work was also partially supported by NSF RTG 1937241.
Publisher Copyright:
© 2021 American Mathematical Society. All rights reserved.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
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U2 - 10.1090/tran/8375
DO - 10.1090/tran/8375
M3 - Article
AN - SCOPUS:85113300107
SN - 0002-9947
VL - 374
SP - 6331
EP - 6366
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 9
ER -