
Special Issue on Symmetry, Separation, Superintegrability and Special
Functions (S^{4})
The Guest Editors for this special issue are
Ernie Kalnins (University of Waikato, Hamilton, New Zealand)
Niky Kamran
(McGill University, Montreal, Canada)
Peter Olver
(University of Minnesota, Minneapolis, USA)
Pavel Winternitz (Universite de Montreal, Canada)
On September 17–19, 2010, the University of Minnesota hosted a
conference honoring Willard Miller, Jr., on the occasion of his
retirement. Entitled “Symmetry, Separation, Superintegrability and
Special Functions” (S^{4} for short), the talks covered Willard's
wideranging research interests, and featured most of his close friends,
collaborators, students, and colleagues. Willard's many fundamental
contributions and influence in these areas have been felt far and wide.
Remarkably, while continuing to be incredibly active throughout his
researcher career, which continues into retirement, he also served in
many administrative capacities at the University of Minnesota, including
Department Head, Associate Director and Director of the I.M.A.,
Associate Dean, and acting Dean. During the meeting, a scholarship fund
for students in a combined Bachelors/Masters' program at Minnesota was
established in Willard's honor. See the conference web site for full
details: http://math.umn.edu/conferences/s4/.
The organizers decided it would be worth assembling a special issue of
SIGMA devoted to the conference's mathematical themes, and agreed to
serve as editors. The 21 papers gathered in this volume represent
contributions closely related to many of the themes of research to which
Willard has made fundamental contributions over the years, including
separation of variables, special functions, integrable systems, and
their associated geometric structures, all of which reflect the wide
spectrum and the remarkable breadth of Willard's scientific interests.
Thus, classical special functions, qspecial functions and harmonic
analysis appear in the contributions of Tom Koornwinder, Luc Vinet and
Alexei Zhedanov, Kurt Bernardo Wolf and Luis Edgar Vicent, Amalia Torre,
Howard Cohl; symmetry and separation of variables are the main theme of
the papers by Antoni Sym and Adam Szereszewski, and Alberto Carignano,
Lorenzo Fatibene, Ray McLenaghan and Giovanni Rastelli, Philip
Broadbridge and Peter Vassiliou; classical and quantum integrable and
superintegrable models are the substance of the papers by Alexander
Turbiner, Yannis Tanoudis and Costas Daskaloyannis, Angel Ballesteros,
Alberto Enciso, Francisco J. Herranz, Orlando Ragnisco and Danilo
Riglioni, Claudia Chanu, Luca Degiovanni and Giovanni Rastelli, Sarah
Post, Christiane Quesne, Ernie G. Kalnins, Jonathan M. Kress and Willard
Miller, Jr.; finally the papers by Michael G. Eastwood and A. Rod Gover,
Charles P. Boyer, Andrei A. Malykh and Mikhail B. Sheftel, Stephen C.
Anco, Sajid Ali and Thomas Wolf, Serge Preston, Yuri Bozhkov and Peter
J. Olver, are related to the more geometric aspects of Willard's
interests, notably the role of symmetries and geometric structures in
differential equations. The high quality of all these papers reflects
the high esteem in which Willard is held by his friends and colleagues
throughout the world. We would like to thank all the authors for these
very fine contributions.
Ernie Kalnins,
Niky Kamran,
Peter Olver,
Pavel Winternitz
Papers in this Issue:

On Darboux's Approach to RSeparability of Variables

Antoni Sym and Adam Szereszewski
SIGMA 7 (2011), 095, 21 pages [ abs
pdf ]

Appell Transformation and Canonical Transforms

Amalia Torre
SIGMA 7 (2011), 072, 34 pages [ abs
pdf ]

From Quantum A_{N} (Calogero) to H_{4} (Rational) Model

Alexander V. Turbiner
SIGMA 7 (2011), 071, 20 pages [ abs
pdf ]

Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction

Stephen C. Anco, Sajid Ali and Thomas Wolf
SIGMA 7 (2011), 066, 10 pages [ abs
pdf ]

Balance Systems and the Variational Bicomplex

Serge Preston
SIGMA 7 (2011), 063, 18 pages [ abs
pdf ]

The BGG Complex on Projective Space

Michael G. Eastwood and A. Rod Gover
SIGMA 7 (2011), 060, 18 pages [ abs
pdf ]

Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on S^{2}×S^{3}

Charles P. Boyer
SIGMA 7 (2011), 058, 22 pages [ abs
pdf ]

Symmetry Operators and Separation of Variables for Dirac's Equation on TwoDimensional Spin Manifolds

Alberto Carignano, Lorenzo Fatibene, Raymond G. McLenaghan and Giovanni Rastelli
SIGMA 7 (2011), 057, 13 pages [ abs
pdf ]

Pohozhaev and Morawetz Identities in Elastostatics and Elastodynamics

Yuri Bozhkov and Peter J. Olver
SIGMA 7 (2011), 055, 9 pages [ abs
pdf ]

Algebraic Calculation of the Energy Eigenvalues for the Nondegenerate ThreeDimensional KeplerCoulomb Potential

Yannis Tanoudis and Costas Daskaloyannis
SIGMA 7 (2011), 054, 11 pages [ abs
pdf ]

The Fourier U(2) Group and Separation of Discrete Variables

Kurt Bernardo Wolf and Luis Edgar Vicent
SIGMA 7 (2011), 053, 18 pages [ abs
pdf ]

The Role of Symmetry and Separation in Surface Evolution and Curve Shortening

Philip Broadbridge and Peter Vassiliou
SIGMA 7 (2011), 052, 19 pages [ abs
pdf ]

On Parameter Differentiation for Integral Representations of Associated Legendre Functions

Howard S. Cohl
SIGMA 7 (2011), 050, 16 pages [ abs
pdf ]

Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform

Ángel Ballesteros, Alberto Enciso, Francisco J. Herranz, Orlando Ragnisco and Danilo Riglioni
SIGMA 7 (2011), 048, 15 pages [ abs
pdf ]

Recursions of Symmetry Orbits and Reduction without Reduction

Andrei A. Malykh and Mikhail B. Sheftel
SIGMA 7 (2011), 043, 13 pages [ abs
pdf ]

On the Limit from qRacah Polynomials to Big qJacobi Polynomials

Tom H. Koornwinder
SIGMA 7 (2011), 040, 8 pages [ abs
pdf ]

First Integrals of Extended Hamiltonians in n+1 Dimensions Generated by Powers of an Operator

Claudia Chanu, Luca Degiovanni and Giovanni Rastelli
SIGMA 7 (2011), 038, 12 pages [ abs
pdf ]

Models of Quadratic Algebras Generated by Superintegrable Systems in 2D

Sarah Post
SIGMA 7 (2011), 036, 20 pages [ abs
pdf ]

Revisiting the Symmetries of the Quantum SmorodinskyWinternitz System in D Dimensions

Christiane Quesne
SIGMA 7 (2011), 035, 21 pages [ abs
pdf ]

A Recurrence Relation Approach to Higher Order Quantum Superintegrability

Ernie G. Kalnins, Jonathan M. Kress and Willard Miller Jr.
SIGMA 7 (2011), 031, 24 pages [ abs
pdf ]

A Bochner Theorem for Dunkl Polynomials

Luc Vinet and Alexei Zhedanov
SIGMA 7 (2011), 020, 9 pages [ abs
pdf ]

