Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 106, 9 pages      arXiv:0711.2401      https://doi.org/10.3842/SIGMA.2007.106
Contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson

Biorthogonal Expansion of Non-Symmetric Jack Functions

Siddhartha Sahi a and Genkai Zhang b
a) Department of Mathematics, Rutgers University, New Brunswick, New Jersey, USA
b) Mathematical Sciences, Chalmers University of Technology and Mathematical Sciences, Göteborg University, Sweden

Received August 08, 2007, in final form October 31, 2007; Published online November 15, 2007

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.

Key words: non-symmetric Jack polynomials and functions; biorthogonal expansion; Laplace transform; Cherednik-Opdam transform.

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