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Elliptic analogue of Vershik-Kerov limit shape

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arxiv 2403.07168 v1 pith:HYGSEOQ4 submitted 2024-03-11 math-ph hep-thmath.COmath.MPmath.PR

Andrey Grekov , Nikita Nekrasov This is my paper · ORCID
classification math-phhep-thmath.COmath.MPmath.PR
keywords measurelimitshapeellipticgaugeplanchereltheoryvershik-kerov
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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 uniform measure, a U(1) case of 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.

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Cited by 2 Pith papers

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  1. Spiralling branes, affine qq-characters and elliptic integrable systems

    hep-th 2024-12 accept novelty 7.0 of 10

    Quantum toroidal algebra intertwiners reproduce Ruijsenaars-Schneider and Koroteev-Shakirov Hamiltonians, Shiraishi functions, and a new proof of the noncommutative Jacobi identity for affine qq-characters.

  2. Quiver BPS Indices from Crystal Profiles

    hep-th 2026-07 conditional novelty 6.5 of 10

    Elliptic genera and lower-dimensional BPS indices equal discrete sums over molecule boundaries in crystals defined by Jeffrey-Kirwan residues, generalizing Nekrasov Young-diagram formulas.

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