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 and NRU HSE, Moscow, Russia)
S. Ole Warnaar (The University of Queensland, Australia)

This issue was inspired by the Workshop Elliptic Hypergeometric Functions in Combinatorics, Integrable Systems and Physics, held at the Erwin Schrödinger Institute for Mathematics and Physics in Vienna, Austria, in March 20–24, 2017.

Elliptic hypergeometric functions are a relatively new class of special functions which first appeared as solutions of the Yang–Baxter equation. Over the last twenty years they have been shown to be related to numerous areas of mathematics and physics, including integrable systems, enumerative and algebraic combinatorics, and quantum field theory. This special issue is devoted to recent developments in the theory of elliptic hypergeometric functions and its applications. It contains 18 original research papers with a total of 517 pages.

The editors of the issue would like to thank all authors for their interesting contributions and the many referees who have assisted us in getting the papers refereed in a timely manner. We would finally like to thank the workshop participants for contributing to the development of the subject.

Michael Schlosser, Vyacheslav Spiridonov and Ole Warnaar        

Papers in this Issue:

Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology
Giovanni Felder, Richárd Rimányi and Alexander Varchenko
SIGMA 14 (2018), 132, 41 pages   [ abs   pdf ]
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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