ALGEBRAIC COMBINATORICS

no. 6
Newell–Littlewood numbers II: extended Horn inequalities
Gao, Shiliang1; Orelowitz, Gidon1; Yong, Alexander1
1 University of Illinois at Urbana-Champaign Dept. of Mathematics 1409 W. Green Street Urbana IL 61801, USA
Algebraic Combinatorics, Volume 5 (2022) no. 6, pp. 1287-1297.

The Newell–Littlewood numbers N μ,ν,λ are tensor product multiplicities of Weyl modules for classical Lie groups, in the stable limit. For which triples of partitions (μ,ν,λ) does N μ,ν,λ >0 hold? The Littlewood–Richardson coefficient case is solved by the Horn inequalities (in work of A. Klyachko and A. Knutson-T. Tao). We extend these celebrated linear inequalities to a much larger family, suggesting a general solution.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.217
Classification: 05E10, 22E46, 15A18
Keywords: Newell–Littlewood numbers, Weyl modules, Horn inequalities
Gao, Shiliang 1; Orelowitz, Gidon 1; Yong, Alexander 1

1 University of Illinois at Urbana-Champaign Dept. of Mathematics 1409 W. Green Street Urbana IL 61801, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Gao, Shiliang; Orelowitz, Gidon; Yong, Alexander. Newell–Littlewood numbers II: extended Horn inequalities. Algebraic Combinatorics, Volume 5 (2022) no. 6, pp. 1287-1297. doi : 10.5802/alco.217. https://alco.centre-mersenne.org/articles/10.5802/alco.217/

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