Vershik-Kerov in higher times
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.
Keywords
Cite
@article{arxiv.2412.18724,
title = {Vershik-Kerov in higher times},
author = {Andrei Grekov and Nikita Nekrasov},
journal= {arXiv preprint arXiv:2412.18724},
year = {2026}
}
Comments
29 pages, v2. final version of the contribution to the "Groups, Geometry, Dynamics" volume dedicated to Anatoly Moiseevich Vershik (1933-2024)