Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Special Issue on Elliptic Hypergeometric Functions and Their Applications

The Guest Editors for this special issue are

Michael J. Schlosser (University of Vienna, Austria)
Vyacheslav P. Spiridonov (JINR, Dubna, Russia)
S. Ole Warnaar (University of Queensland, Australia)

Topics for this special issue will include:

  • general theory of elliptic hypergeometric functions;
  • univariate and multivariate elliptic hypergeometric (bi-)orthogonal functions;
  • combinatorics of elliptic hypergeometric functions and applications in probability theory;
  • elliptic determinants and theta functions on root systems;
  • elliptic integrable systems, elliptic Painlevé equations and isomonodromy problems;
  • elliptic hypergeometric integrals and superconformal indices in quantum field theory;
  • applications in quantum mechanics and statistical mechanics.

This issue is partially related to the Workshop Elliptic Hypergeometric Functions in Combinatorics, Integrable Systems and Physics at the Erwin Schrödinger Institute for Mathematics and Physics in Vienna, Austria, in March 20–24, 2017.

Workshop participants and others whose work is concerned with the above topics are invited to submit papers to the special issue. For this issue, both original research articles and review papers are welcome.

There are no paper length limits to the submitted works. Deadline for the submission is January 31, 2018.

All articles will go through the standard peer reviewing procedure of SIGMA.

Papers in this Issue:

Matrix Bailey Lemma and the Star-Triangle Relation
Kamil Yu. Magadov and Vyacheslav P. Spiridonov
SIGMA 14 (2018), 121, 13 pages   [ abs   pdf ]
Macdonald Polynomials of Type $C_n$ with One-Column Diagrams and Deformed Catalan Numbers
Ayumu Hoshino and Jun'ichi Shiraishi
SIGMA 14 (2018), 101, 33 pages   [ abs   pdf ]
Connection Formula for the Jackson Integral of Type $A_n$ and Elliptic Lagrange Interpolation
Masahiko Ito and Masatoshi Noumi
SIGMA 14 (2018), 077, 42 pages   [ abs   pdf ]
The Functional Method for the Domain-Wall Partition Function
Jules Lamers
SIGMA 14 (2018), 064, 23 pages   [ abs   pdf ]
On $q$-Deformations of the Heun Equation
Kouichi Takemura
SIGMA 14 (2018), 061, 16 pages   [ abs   pdf ]
The Determinant of an Elliptic Sylvesteresque Matrix
Gaurav Bhatnagar and Christian Krattenthaler
SIGMA 14 (2018), 052, 15 pages   [ abs   pdf ]
The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory
Arash Arabi Ardehali
SIGMA 14 (2018), 043, 30 pages   [ abs   pdf ]
Surface Defects in E-String Compactifications and the van Diejen Model
Belal Nazzal and Shlomo S. Razamat
SIGMA 14 (2018), 036, 20 pages   [ abs   pdf ]
Elliptically Distributed Lozenge Tilings of a Hexagon
Dan Betea
SIGMA 14 (2018), 032, 39 pages   [ abs   pdf ]
${\rm SL}(2,\mathbb{C})$ Gustafson Integrals
Sergey É. Derkachov, Alexander N. Manashov and Pavel A. Valinevich
SIGMA 14 (2018), 030, 16 pages   [ abs   pdf ]
Elliptic Well-Poised Bailey Transforms and Lemmas on Root Systems
Gaurav Bhatnagar and Michael J. Schlosser
SIGMA 14 (2018), 025, 44 pages   [ abs   pdf ]
Multivariate Quadratic Transformations and the Interpolation Kernel
Eric M. Rains
SIGMA 14 (2018), 019, 69 pages   [ abs   pdf ]
Elliptic Hypergeometric Sum/Integral Transformations and Supersymmetric Lens Index
Andrew P. Kels and Masahito Yamazaki
SIGMA 14 (2018), 013, 29 pages   [ abs   pdf ]
Series Solutions of the Non-Stationary Heun Equation
Farrokh Atai and Edwin Langmann
SIGMA 14 (2018), 011, 32 pages   [ abs   pdf ]
Elliptic Determinantal Processes and Elliptic Dyson Models
Makoto Katori
SIGMA 13 (2017), 079, 36 pages   [ abs   pdf ]
An Elliptic Garnier System from Interpolation
Yasuhiko Yamada
SIGMA 13 (2017), 069,  8 pages   [ abs   pdf ]
Gustafson-Rakha-Type Elliptic Hypergeometric Series
Hjalmar Rosengren
SIGMA 13 (2017), 037, 11 pages   [ abs   pdf ]

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