A new integral formula for Heckman-Opdam hypergeometric functions

作者：Sun Yi^*

来源：Advances in Mathematics, 2016, 289: 1157-1204.

DOI：10.1016/j.aim.2015.11.037

• Heckman-Opdam hypergeometric functions
• Quasiclassical limit
• Rational Cherednik algebra
• Calogero-Moser system
• Gelfand-Tsetlin coordinates
• Poisson-Lie groups

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.

• 出版日期2016-2-5
• 单位MIT