A New Integral Formula for Heckman-opdam Hypergeometric Functions
نویسنده
چکیده
We provide Harish-Chandra type formulas for the multivariate Bessel functions and HeckmanOpdam 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. in [EK94]. 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 [BG13] of Borodin-Gorin on the β-Jacobi corners ensemble.
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تاریخ انتشار 2015