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

Special Issue on Exact Solvability and Symmetry Avatars in honour of Luc Vinet

The Guest Editors for this special issue are

Vincent Genest (Université de Montréal, Canada)
Decio Levi (Università degli Studi Roma Tre, Italy)
Willard Miller (University of Minnesota, USA)
Yvan Saint-Aubin (Université de Montréal, Canada)
Pavel Winternitz (Université de Montréal, Canada)

Luc Vinet's scientific career now embraces more than thirty-five years. His research has had an impact on many topics in theoretical and mathematical physics. Its main themes are symmetries in physics and their underlying algebraic structures. These were present in his very first works, the geometric description of invariant gauge fields and the study of early examples of supersymmetric quantum-mechanical systems. And these themes are the threads weaving the present special issue together: integrable and exactly solvable models, algebraic combinatorics, field and string theory, quantum information, orthogonal polynomials and superintegrability. Not surprisingly Luc has made significant contributions in all these domains.

The diversity of fields and the number of authors of this special issue, as well as those of the participants at the conference Exact Solvability and Symmetry Avatars celebrating his 60th birthday and held at the Centre de recherches mathématiques in August 2014, are witnesses of the impact Luc has had on our community. This impact goes beyond the impressive breadth of his published works: Luc has influenced many scientific careers by being a great colleague, collaborator and mentor, and by playing an active role in the development of many opportunities for the community. We are extremely happy to dedicate this special issue of SIGMA to him, with admiration and friendship.

Vincent Genest, Decio Levi, Willard Miller Jr, Yvan Saint-Aubin, Pavel Winternitz        

Papers in this Issue:

Multispecies Weighted Hurwitz Numbers
J. Harnad
SIGMA 11 (2015), 097, 19 pages   [ abs   pdf ]
Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests
Decio Levi, Luigi Martina and Pavel Winternitz
SIGMA 11 (2015), 080, 20 pages   [ abs   pdf ]
Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators
Tom H. Koornwinder
SIGMA 11 (2015), 074, 22 pages   [ abs   pdf ]
A CA Hybrid of the Slow-to-Start and the Optimal Velocity Models and its Flow-Density Relation
Hideaki Ujino and Tetsu Yajima
SIGMA 11 (2015), 065, 10 pages   [ abs   pdf ]
Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials
Yves Grandati and Christiane Quesne
SIGMA 11 (2015), 061, 26 pages   [ abs   pdf ]
Racah Polynomials and Recoupling Schemes of $\mathfrak{su}(1,1)$
Sarah Post
SIGMA 11 (2015), 057, 17 pages   [ abs   pdf ]
From Jack to Double Jack Polynomials via the Supersymmetric Bridge
Luc Lapointe and Pierre Mathieu
SIGMA 11 (2015), 051, 15 pages   [ abs   pdf ]
Embeddings of the Racah Algebra into the Bannai-Ito Algebra
Vincent X. Genest, Luc Vinet and Alexei Zhedanov
SIGMA 11 (2015), 050, 11 pages   [ abs   pdf ]
Higher Order Deformations of Complex Structures
Eric D'Hoker and Duong H. Phong
SIGMA 11 (2015), 047, 14 pages   [ abs   pdf ]
On the Integrability of Supersymmetric Versions of the Structural Equations for Conformally Parametrized Surfaces
Sébastien Bertrand, Alfred M. Grundland and Alexander J. Hariton
SIGMA 11 (2015), 046, 16 pages   [ abs   pdf ]
Time and Band Limiting for Matrix Valued Functions, an Example
F. Alberto Grünbaum, Inés Pacharoni and Ignacio Nahuel Zurrián
SIGMA 11 (2015), 044, 14 pages   [ abs   pdf ]
Structure Relations and Darboux Contractions for 2D 2nd Order Superintegrable Systems
Robin Heinonen, Ernest G. Kalnins, Willard Miller Jr. and Eyal Subag
SIGMA 11 (2015), 043, 33 pages   [ abs   pdf ]
From Twisted Quantum Loop Algebras to Twisted Yangians
Patrick Conner and Nicolas Guay
SIGMA 11 (2015), 040, 14 pages   [ abs   pdf ]
The Combinatorics of Associated Laguerre Polynomials
Jang Soo Kim and Dennis Stanton
SIGMA 11 (2015), 039, 12 pages   [ abs   pdf ]
Quantum Integrals for a Semi-Infinite q-Boson System with Boundary Interactions
Jan Felipe van Diejen and Erdal Emsiz
SIGMA 11 (2015), 037,  9 pages   [ abs   pdf ]
Exact M-Theory Solutions, Integrable Systems, and Superalgebras
Eric D'Hoker
SIGMA 11 (2015), 029, 20 pages   [ abs   pdf ]
On the q-Charlier Multiple Orthogonal Polynomials
Jorge Arvesú and Andys M. Ramírez-Aberasturis
SIGMA 11 (2015), 026, 14 pages   [ abs   pdf ]
Fourier and Gegenbauer Expansions for a Fundamental Solution of Laplace's Equation in Hyperspherical Geometry
Howard S. Cohl and Rebekah M. Palmer
SIGMA 11 (2015), 015, 23 pages   [ abs   pdf ]

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