A new integral formula for Heckman-Opdam hypergeometric functions
Abstract
We provide Harish-Chandra type formulas for the multivariate Bessel functions and Heckman-Opdam hypergeometric functions as representation-valued integrals over dressing orbits. Our expression is the quasi-classical limit of the realization of Macdonald polynomials as traces of intertwiners of quantum groups given by Etingof-Kirillov Jr. Integration over the Liouville tori of the Gelfand-Tsetlin integrable system and adjunction for higher Calogero-Moser Hamiltonians recovers and gives a new proof of the integral realization over Gelfand-Tsetlin polytopes which appeared in the recent work of Borodin-Gorin on the beta-Jacobi corners ensemble.
Cite
@article{arxiv.1406.3772,
title = {A new integral formula for Heckman-Opdam hypergeometric functions},
author = {Yi Sun},
journal= {arXiv preprint arXiv:1406.3772},
year = {2015}
}
Comments
30 pages. v4: corrected sign convention in definition of CM Hamiltonians and Dunkl operators; corrected computations of adjoints in Sections 4 and 5; main results are unchanged