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arXiv · 1608.06215

Maximal rank subgroups and strong functoriality of the additive eigencone

Michael Schuster
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Abstract

Let $G$ be a simple connected complex Lie group. The additive eigencone of $G$ is a polyhedral cone containing the set of solutions to the additive eigenvalue problem, a generalization of the Hermitian eigenvalue problem. The additive eigencone is functorial, and for certain subgroups satisfies a stronger functoriality property: the eigencone of the subgroup is determined by the inequalities of the larger eigencone. Belkale and Kumar first studied this property for subgroups invariant under a diagram automorphism of $G$. We study a new class of subgroups arising from centralizers of torus elements that have the strong eigencone functoriality property.

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Michael Schuster. 2016-08-22. Maximal rank subgroups and strong functoriality of the additive eigencone. https://arxiv.org/abs/1608.06215

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