Yi Sun
Published 2014-06-14, updated 2015-01-31Version 2
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.
Comments: 27 pages. v2: added Section 3 on the quasi-classical limit; corrected normalization of Heckman-Opdam hypergeometric functions; added some references
Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC
Integral representation and sharp asymptotic results for some Heckman-Opdam hypergeometric functions of type BC
A representation-theoretic proof of the branching rule for Macdonald polynomials
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