Year: 2023
Type: preprint
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 $G$.
Source: arXiv (Cornell University)
Authors: Belkale, Prakash, Kiers, Joshua
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4382765783