Newell-Littlewood numbers III: eigencones and GIT-semigroups
Algebraic Geometry
2022-06-24 v2 Combinatorics
Representation Theory
Abstract
The Newell-Littlewood numbers are tensor product multiplicities of Weyl modules for the classical groups in the stable range. Littlewood-Richardson coefficients form a special case. Klyachko connected eigenvalues of sums of Hermitian matrices to the saturated LR-cone and established defining linear inequalities. We prove analogues for the saturated NL-cone: an eigenvalue interpretation; a minimal list of defining linear inequalities; a description by Extended Horn inequalities, as conjectured in part II of this series; and a factorization of NL-numbers, on the boundary.
Keywords
Cite
@article{arxiv.2107.03152,
title = {Newell-Littlewood numbers III: eigencones and GIT-semigroups},
author = {Shiliang Gao and Gidon Orelowitz and Nicolas Ressayre and Alexander yong},
journal= {arXiv preprint arXiv:2107.03152},
year = {2022}
}
Comments
21 pagesv2 has a significantly shorter argument for a stronger version of Theorem 1.5, using a result of R. King