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A 'missing' family of classical orthogonal polynomials
We study a family of 'classical' orthogonal polynomials which satisfy (apart from a three-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl type. These polynomialsExpand
Exact operator solution of the Calogero-Sutherland model
The wave functions of the Calogero-Sutherland model are known to be expressible in terms of Jack polynomials. A formula which allows to obtain the wave functions of the excited states by acting withExpand
The Quantum Dynamics of the Compactified Trigonometric Ruijsenaars–Schneider Model
Abstract:We quantize a compactified version of the trigonometric Ruijsenaars–Schneider particle model with a phase space that is symplectomorphic to the complex projective space ℂℙN. The quantumExpand
Group actions on principal bundles and invariance conditions for gauge fields
Invariance conditions for gauge fields under smooth group actions are interpreted in terms of invariant connections on principal bundles. A classification of group actions on bundles as automorphismsExpand
Algebraic methods and q-special functions
Science fiction and Macdonald's polynomials by F. Bergeron and A. M. Garsia On the expansion of elliptic functions and applications by R. Chouikha Generalized hypergeometric functions-ClassificationExpand
A Dirac–Dunkl Equation on S2 and the Bannai–Ito Algebra
The Dirac–Dunkl operator on the two-sphere associated to the $${{\mathbb{Z}_{2}^{3}}}$$Z23 reflection group is considered. Its symmetries are found and are shown to generate the Bannai–Ito algebra.Expand
Quantum symmetries of q‐difference equations
A general method is presented to determine the symmetry operators of linear q‐difference equations. It is applied to q‐difference analogs of the Helmoltz, heat, and wave equations in diverseExpand
Analytic next-to-nearest-neighbor X X models with perfect state transfer and fractional revival
Certain nonuniformly coupled spin chains can exhibit perfect transfer of quantum states from end to end. Motivated by recent experimental implementations in evanescently coupled waveguide arrays, weExpand
Representations of the Schrödinger group and matrix orthogonal polynomials
The representations of the Schrodinger group in one space dimension are explicitly constructed in the basis of the harmonic oscillator states. These representations are seen to involve matrixExpand