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Funktsional'nyi Analiz i ego Prilozheniya, 2024, Volume 58, Issue 2, Pages 52–71
DOI: https://doi.org/10.4213/faa4202 (Mi faa4202) 		 
Elliptic analogue of the Vershik–Kerov limit shape

Andrei Grekova, Nikita Nekrasovba

a Yang Institute for Theoretical Physics, Stony Brook University
b Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, USA
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DOI: https://doi.org/10.4213/faa4202
Abstract: We review the limit shape problem for the Plancherel measure and its generalizations found in supersymmetric gauge theory instanton count. We focus on the measure, interpolating between the Plancherel measure and the uniform measure, a $U(1)$ case of $\mathcal{N}=2^{*}$ gauge theory. We give the formula for its limit shape in terms of elliptic functions, generalizing the trigonometric “arcsin” law of Vershik–Kerov and Logan–Schepp.
Keywords: limit measures, limit shape, spectral curves, instantons, enumerative geometry.
Funding agency Grant number
National Science Foundation 2310279
Research is partly supported by NSF PHY Award 2310279.
Received: 05.02.2024
Revised: 11.03.2024
Accepted: 18.03.2024
Published: 30.04.2024
English version:
Functional Analysis and Its Applications, 2024, Volume 58, Issue 2, Pages 143–159
DOI: https://doi.org/10.1134/S0016266324020059
Bibliographic databases:
Document Type: Article
MSC: 60F15, 14H81, 81Q60
Language: Russian
Citation: Andrei Grekov, Nikita Nekrasov, “Elliptic analogue of the Vershik–Kerov limit shape”, Funktsional. Anal. i Prilozhen., 58:2 (2024), 52–71; Funct. Anal. Appl., 58:2 (2024), 143–159
Citation in format AMSBIB
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