A ‘missing’ family of classical orthogonal polynomials
- L. Vinet, A. Zhedanov
- Mathematics
- 7 November 2010
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 polynomials…
Exact operator solution of the Calogero-Sutherland model
- L. Lapointe, L. Vinet
- Mathematics
- 5 September 1995
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 with…
The Quantum Dynamics of the Compactified Trigonometric Ruijsenaars–Schneider Model
- J. F. van Diejen, L. Vinet
- Mathematics
- 15 September 1997
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 quantum…
Symmetries and degeneracies of a charged oscillator in the field of a magnetic monopole
- Simon Labelle, M. Mayrand, L. Vinet
- Physics
- 1 June 1991
The constants of motion responsible for the level degeneracy of a charged, spin 0 particle subjected to harmonic and centrifugal forces and to the field of a magnetic monopole are obtained. Operators…
Advances in mathematical sciences : CRM's 25 years
- L. Vinet
- Mathematics
- 17 October 1997
The problem of classifying automorphic representations of classical groups by J. G. Arthur A survey of results relating to Giuga's conjecture on primality by J. M. Borwein and E. Wong Solving…
Group actions on principal bundles and invariance conditions for gauge fields
- J. Harnad, S. Shnider, L. Vinet
- Mathematics
- 1 December 1980
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 automorphisms…
Superintegrability in Two Dimensions and the Racah–Wilson Algebra
- Vincent X. Genest, L. Vinet, A. Zhedanov
- Mathematics
- 21 July 2013
The analysis of the most general second-order superintegrable system in two dimensions: the generic 3-parameter model on the 2-sphere is cast in the framework of the Racah problem for the…
More on the q-oscillator algebra and q-orthogonal polynomials
- R. Floreanini, J. Letourneux, L. Vinet
- Mathematics
- 26 April 1995
Properties of certain q-orthogonal polynomials are connected to the q-oscillator algebra. The Wall and q-Laguerre polynomials are shown to arise as matrix elements of q-exponentials of the generators…
CMV Matrices and Little and Big −1 Jacobi Polynomials
- M. Derevyagin, L. Vinet, A. Zhedanov
- Mathematics
- 17 August 2011
We introduce a new map from polynomials orthogonal on the unit circle to polynomials orthogonal on the real axis. This map is closely related to the theory of CMV matrices. It contains an arbitrary…
Automorphisms of the Heisenberg–Weyl algebra and d-orthogonal polynomials
- L. Vinet, A. Zhedanov
- Mathematics
- 26 March 2009
We show that the d-orthogonal Charlier and Hermite polynomials appear naturally as matrix elements of nonunitary transformations corresponding to automorphisms of the Heisenberg–Weyl (oscillator)…
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