Vertices in multiplicative eigenvalue problem for arbitrary groups

2023/06/29 by Belkale, Prakash, Kiers, Joshua
#14H60 #14M15 #14N35 #15A42 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2306.16676

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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