Vertices in multiplicative eigenvalue problem for arbitrary groups

Author:

Prakash Belkale, Joshua Kiers

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Representation Theory (math.RT)

journal:

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date:

2023-06-28 16:00:00

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 $G$.