Biorthogonal Expansion of Non-Symmetric Jack Functions

Abstract

We find a biorthogonal expansion of the Cayley transform of the non-symmetric Jack functions in terms of the non-symmetric Jack polynomials, the coefficients being Meixner-Pollaczek type polynomials. This is done by computing the Cherednik-Opdam transform of the non-symmetric Jack polynomials multiplied by the exponential function.

This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (5)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• The Calogero-Sutherland Model and Generalized Classical Polynomials
• A recursion and a combinatorial formula for Jack polynomials
• A new scalar product for nonsymmetric Jack polynomials
• Spherical transform and Jacobi polynomials on root systems of type BC

Cited by in corpus (1)

• Hermitian Symmetric Spaces of Tube Type and Multivariate Meixner-Pollaczek Polynomials