Elliptic Selberg integrals
- J. F. van Diejen, V. Spiridonov
- Mathematics
- 2001
We introduce new Selberg-type multidimensional integrals built of Ruijsenaars' elliptic gamma functions. We show that the vanishing of our integrals for a specific parameter hypersurface implies…
Integrability of difference Calogero-Moser systems
- J. F. van Diejen
- Mathematics
- 1 June 1994
A general class of n‐particle difference Calogero–Moser systems with elliptic potentials is introduced. Besides the step size and two periods, the Hamiltonian depends on nine coupling constants. We…
Difference Calogero-Moser systems and finite Toda chains
- J. F. van Diejen
- Mathematics, Physics
- 1 March 1995
Limits of a recently introduced n‐particle difference Calogero–Moser system with elliptic potentials are studied. We obtain hyperbolic and rational difference Calogero–Moser systems with an…
An Elliptic Macdonald-Morris Conjecture and Multiple Modular Hypergeometric Sums
- J. F. van Diejen, V. Spiridonov
- Mathematics
- 2000
We present an elliptic Macdonald-Morris constant term conjecture in the form of an evaluation formula for a Selberg-type multiple beta integral com- posed of elliptic gamma functions. By multivariate…
On certain multiple Bailey, Rogers and Dougall type summation formulas
- J. F. van Diejen
- Mathematics
- 1 September 1997
A multidimensional generalization of Bailey's very-well-poised bi- lateral basic hypergeometric 6 6 summation formula and its Dougall type 5H5 hypergeometric degeneration for q ! 1 is studied. The…
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…
Unit Circle Elliptic Beta Integrals
- J. F. van Diejen, V. Spiridonov
- Mathematics
- 17 September 2003
We present some elliptic beta integrals with a base parameter on the unit circle, together with their basic degenerations.
Self-dual Koornwinder-Macdonald polynomials
- J. F. van Diejen
- Mathematics
- 1996
We prove certain duality properties and present recurrence relations for a four-parameter family of self-dual Koornwinder-Macdonald polynomials. The recurrence relations are used to verify…
Commuting difference operators with polynomial eigenfunctions
- J. F. van Diejen
- Mathematics
- 7 June 1993
We present explicit generators of an algebra of commuting difference operators with trigonometric coefficients. The operators are simultaneously diagonalized by recently discovered q-polynomials…
On the Plancherel Formula for the (Discrete) Laplacian in a Weyl Chamber with Repulsive Boundary Conditions at the Walls
- J. F. van Diejen
- Mathematics
- 1 February 2004
It is known from early work of Gaudin that the quantum system of n Bosonic particles on the line with a pairwise delta-potential interaction admits a natural generalization in terms of the root…
...
...