xiv
Contents
A New Approach to Analysis of 2D Higher Order Quantum
Superintegrable Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Bjorn K. Berntson, Ian Marquette, and Willard Miller, Jr.
Ladder Operators and Rational Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
David Gómez-Ullate, Yves Grandati, Zoé McIntyre, and Robert Milson
Tachyons and Representations of Sp(2, R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
P. Moylan
A Confined Quasi-Maximally Superintegrable N-dimensional
System, Classical and Quantum, in a Space with Variable Curvature . . . . . 141
Orlando Ragnisco
Conditional Discretization of a Generalized Reaction–Diffusion
Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Decio Levi, Miguel A. Rodríguez, and Zora Thomova
Discrete Curve Flows in Two-Dimensional Cayley–Klein Geometries . . . . . 157
Joseph Benson and Francis Valiquette
Zernike System Stems from Free Motion on the 3-Sphere . . . . . . . . . . . . . . . . . . 169
Kurt Bernardo Wolf, Natig M. Atakishiyev, George S. Pogosyan,
and Alexander Yakhno
Part II Algebraic and Non-perturbative Methods
W-Algebras via Lax Type Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Daniele Valeri
Color Algebraic Extension of Supersymmetric Quantum Mechanics. . . . . . 199
Naruhiko Aizawa, Kosuke Amakawa, and Shunya Doi
The Racah Algebra and sl n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Hendrik De Bie, Luc Vinet, and Wouter van de Vijver
On Reducible Verma Modules over Jacobi Algebra . . . . . . . . . . . . . . . . . . . . . . . . . 217
V. K. Dobrev
Howe Duality and Algebras of the Askey–Wilson Type: An Overview . . . . 225
Julien Gaboriaud, Luc Vinet, and Stéphane Vinet
Second-Order Supersymmetric Partners of the Trigonometric
Rosen–Morse Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Rosa Reyes, D.J. Fernández, and H. Gasperín
A Noncommutative Geometric Approach to the Batalin–Vilkovisky
Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Roberta A. Iseppi
A New Method for Constructing Squeezed States for the Isotropic
2D Harmonic Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
James Moran and Véronique Hussin
Contents
A New Approach to Analysis of 2D Higher Order Quantum
Superintegrable Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Bjorn K. Berntson, Ian Marquette, and Willard Miller, Jr.
Ladder Operators and Rational Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
David Gómez-Ullate, Yves Grandati, Zoé McIntyre, and Robert Milson
Tachyons and Representations of Sp(2, R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
P. Moylan
A Confined Quasi-Maximally Superintegrable N-dimensional
System, Classical and Quantum, in a Space with Variable Curvature . . . . . 141
Orlando Ragnisco
Conditional Discretization of a Generalized Reaction–Diffusion
Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Decio Levi, Miguel A. Rodríguez, and Zora Thomova
Discrete Curve Flows in Two-Dimensional Cayley–Klein Geometries . . . . . 157
Joseph Benson and Francis Valiquette
Zernike System Stems from Free Motion on the 3-Sphere . . . . . . . . . . . . . . . . . . 169
Kurt Bernardo Wolf, Natig M. Atakishiyev, George S. Pogosyan,
and Alexander Yakhno
Part II Algebraic and Non-perturbative Methods
W-Algebras via Lax Type Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Daniele Valeri
Color Algebraic Extension of Supersymmetric Quantum Mechanics. . . . . . 199
Naruhiko Aizawa, Kosuke Amakawa, and Shunya Doi
The Racah Algebra and sl n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Hendrik De Bie, Luc Vinet, and Wouter van de Vijver
On Reducible Verma Modules over Jacobi Algebra . . . . . . . . . . . . . . . . . . . . . . . . . 217
V. K. Dobrev
Howe Duality and Algebras of the Askey–Wilson Type: An Overview . . . . 225
Julien Gaboriaud, Luc Vinet, and Stéphane Vinet
Second-Order Supersymmetric Partners of the Trigonometric
Rosen–Morse Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Rosa Reyes, D.J. Fernández, and H. Gasperín
A Noncommutative Geometric Approach to the Batalin–Vilkovisky
Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Roberta A. Iseppi
A New Method for Constructing Squeezed States for the Isotropic
2D Harmonic Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
James Moran and Véronique Hussin