A new integral formula for Heckman-Opdam hypergeometric functions

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• 作者：Yi Sun ^{yisun@math.mit.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Heckman&ndash ; Opdam hypergeometric functions ; Quasiclassical limit ; Rational Cherednik algebra ; Calogero&ndash ; Moser system ; Gelfand&ndash ; Tsetlin coordinates ; Poisson&ndash ; Lie groups
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：5 February 2016
• 年：2016
• 卷：289
• 期：Complete
• 页码：1157-1204
• 全文大小：683 K

文摘

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 β-Jacobi corners ensemble.