Year: 2024
Type: preprint
Abstract: Several generalizations of Vershik-Kerov limit shape problem are motivated by topological string theory and supersymmetric gauge theory instanton count. In this paper specifically we study the circular and linear quiver theories. We also briefly discuss the double-elliptic generalization of the Vershik-Kerov problem, related to six dimensional gauge theory compactified on a torus, and to elliptic cohomology of the Hilbert scheme of points on a plane. We prove that the limit shape in that setting is governed by a genus two algebraic curve, suggesting unexpected dualities between the enumerative and equivariant parameters.
Source: arXiv (Cornell University)
Authors: Grekov, Andrei, Nekrasov, Nikita
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405900246