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arXiv · 2306.16676

Vertices in multiplicative eigenvalue problem for arbitrary groups

Prakash Belkale·Joshua Kiers
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Abstract

We determine, in an inductive framework, the vertices of the polytope $P(s,K)$ controlling the conjugacy classes of elements which product to one in the maximal compact subgroup $K$ of a simple complex algebraic group $G$. This extends earlier work of the authors in related contexts. One feature of this work is the use of Kontsevich compactifications of the moduli of $P$-bundles (replacing the use of quot schemes in type A) which are related to semi-infinite geometry. We also obtain a quantum generalization of Fulton's conjecture valid for all $G$.

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Prakash Belkale, Joshua Kiers. 2023-06-29. Vertices in multiplicative eigenvalue problem for arbitrary groups. https://arxiv.org/abs/2306.16676

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