Elliptic Analogue of the Vershik–Kerov Limit Shape

Andrei Grekov; Nikita Nekrasov

doi:10.1134/S0016266324020059

Elliptic Analogue of the Vershik–Kerov Limit Shape

Andrei Grekov
, Nikita Nekrasov

Simons Center for Geometry & Physics

Stony Brook University

Research output: Contribution to journal › Article › peer-review

Abstract

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 case of 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.

Original language	English
Pages (from-to)	143-159
Number of pages	17
Journal	Functional Analysis and its Applications
Volume	58
Issue number	2
DOIs	https://doi.org/10.1134/S0016266324020059
State	Published - Jun 2024

Keywords

14H81
60F15
81Q60
enumerative geometry
instantons
limit measures
limit shape
spectral curves

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10.1134/S0016266324020059

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abstract = "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 case of 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.",

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AU - Nekrasov, Nikita

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N2 - 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 case of 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.

AB - 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 case of 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.

KW - 14H81

KW - 60F15

KW - 81Q60

KW - enumerative geometry

KW - instantons

KW - limit measures

KW - limit shape

KW - spectral curves

UR - https://www.scopus.com/pages/publications/85199215185

U2 - 10.1134/S0016266324020059

DO - 10.1134/S0016266324020059

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SP - 143

EP - 159

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

IS - 2

ER -

Elliptic Analogue of the Vershik–Kerov Limit Shape

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Keywords

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