V. P. Spiridonov, “Elliptic hypergeometric functions and Calogero–Sutherland-type models”, TMF, 150:2 (2007), 311–324; Theoret. and Math. Phys., 150:2 (2007), 266

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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 150, Number 2, Pages 311–324
DOI: https://doi.org/10.4213/tmf5981 (Mi tmf5981)

This article is cited in 24 scientific papers (total in 24 papers)

Elliptic hypergeometric functions and Calogero–Sutherland-type models

V. P. Spiridonov

Joint Institute for Nuclear Research

Full-text PDF (436 kB) Citations (24)

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DOI: https://doi.org/10.4213/tmf5981

Abstract: We consider an elliptic analogue of the Gauss hypergeometric function and two of its multivariate generalizations. We describe their relation to elliptic beta integrals, the exceptional Weyl group

E_{7}

$E_7$ , the elliptic hypergeometric equation, and Calogero–Sutherland-type models.

Keywords: completely integrable system, Calogero–Sutherland model, hypergeometric function, elliptic function.

Received: 01.05.2006

English version:
Theoretical and Mathematical Physics, 2007, Volume 150, Issue 2, Pages 266–277
DOI: https://doi.org/10.1007/s11232-007-0020-5

Bibliographic databases:

Language: Russian

Citation: V. P. Spiridonov, “Elliptic hypergeometric functions and Calogero–Sutherland-type models”, TMF, 150:2 (2007), 311–324; Theoret. and Math. Phys., 150:2 (2007), 266–277

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf5981

https://doi.org/10.4213/tmf5981

https://www.mathnet.ru/eng/tmf/v150/i2/p311

This publication is cited in the following 24 articles:

Martin Hallnäs, Edwin Langmann, Encyclopedia of Mathematical Physics, 2025, 83
G.A. Sarkissian, V.P. Spiridonov, “Complex and rational hypergeometric functions on root systems”, Journal of Geometry and Physics, 203 (2024), 105274
Elena Apresyan, Gor Sarkissian, Vyacheslav P. Spiridonov, “A parafermionic hypergeometric function and supersymmetric 6j-symbols”, Nuclear Physics B, 990 (2023), 116170
S. E. Derkachov, G. A. Sarkissian, V. P. Spiridonov, “Elliptic hypergeometric function and $6j$ -symbols for the $SL(2,\pmb{\mathbb C})$ group”, Theoret. and Math. Phys., 213:1 (2022), 1406–1422
Jan Felipe van Diejen, Tamás Görbe, “Elliptic Racah polynomials”, Lett Math Phys, 112:4 (2022)
G A Sarkissian, V P Spiridonov, “Complex hypergeometric functions and integrable many-body problems”, J. Phys. A: Math. Theor., 55:38 (2022), 385203
Jan Felipe van Diejen, Tamás Görbe, “Eigenfunctions of a Discrete Elliptic Integrable Particle Model with Hyperoctahedral Symmetry”, Commun. Math. Phys., 392:1 (2022), 279
Tsujimoto S., Vinet L., Zhedanov A., “The Rational Heun Operator and Wilson Biorthogonal Functions”, Ramanujan J., 2021
Vyacheslav P. Spiridonov, Moscow Lectures, 5, Partition Functions and Automorphic Forms, 2020, 271
Spiridonov V.P., “Rarefied Elliptic Hypergeometric Functions”, Adv. Math., 331 (2018), 830–873
Bruenner F., Regalado D., Spiridonov V.P., “Supersymmetric Casimir Energy and Sl(3, Z) Transformations”, J. High Energy Phys., 2017, no. 7, 041
Maruyoshi K., Yagi J., “Surface defects as transfer matrices”, Prog. Theor. Exp. Phys., 2016, no. 11, 113B01
Bruenner F., Spiridonov V.P., “A duality web of linear quivers”, Phys. Lett. B, 761 (2016), 261–264
Spiridonov V.P., Vartanov G.S., “Elliptic Hypergeometry of Supersymmetric Dualities II. Orthogonal Groups, Knots, and Vortices”, Commun. Math. Phys., 325:2 (2014), 421–486
Gadde A. Rastelli L. Razamat Sh.S. Yan W., “Gauge Theories and Macdonald Polynomials”, Commun. Math. Phys., 319:1 (2013), 147–193
Gaiotto D. Rastelli L. Razamat Sh.S., “Bootstrapping the Superconformal Index with Surface Defects”, J. High Energy Phys., 2013, no. 1, 022
Rains E.M., “Elliptic Littlewood Identities”, J. Comb. Theory Ser. A, 119:7 (2012), 1558–1609
Spiridonov V.P., “Elliptic Beta Integrals and Solvable Models of Statistical Mechanics”, Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, Contemporary Mathematics, 563, ed. AcostaHumanez P. Finkel F. Kamran N. Olver P., Amer Mathematical Soc, 2012, 181–211
Spiridonov V.P., Vartanov G.S., “Elliptic Hypergeometry of Supersymmetric Dualities”, Comm Math Phys, 304:3 (2011), 797–874
Dolan F.A.H., Spiridonov V.P., Vartanov G.S., “From 4d superconformal indices to 3d partition functions”, Phys Lett B, 704:3 (2011), 234–241

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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