摘要 : 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 r... 展开 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 and Kirillov Jr. in [10]. 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 [4] of Borodin and Gorin on the beta-Jacobi corners ensemble. (C) 2015 Elsevier Inc. All rights reserved. 收起