Siddhartha Sahi, G. Zhang, “Biorthogonal Expansion of Non-Symmetric Jack Functions”, SIGMA, 2007, Volume 3,106, 9 pp.

This article is cited in 3 papers

Biorthogonal Expansion of Non-Symmetric Jack Functions

Siddhartha Sahi^a, G. 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

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.

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

MSC: 33C52; 33C67; 43A90

Received: August 8, 2007; in final form October 31, 2007; Published online November 15, 2007

Language: English

DOI: 10.3842/SIGMA.2007.106