Mathematical problems of nonlinearity

On the Structure of Zonal Spherical Functions on Symmetric Spaces of Negative Curvature of Type AII

V. I. Inozemtsev

Laboratory of Theoretical Physics, JINR, ul. Universitetskaya 19, Dubna, 141980 Moscow Region, Russia

Abstract: A purely algebraic method is proposed for the construction of zonal spherical functions (ZSF) on symmetric spaces $X_{n}^{-}=SL(n,Q)/Sp(n)$ and eigenfunctions of the hyperbolic Sutherland operator connected with them. Examples of the explicit calculations of the coefficients determining the structure of ZSF are given.

Keywords: hyperbolic Sutherland operator, permutation group, zonal spherical functions.

MSC: 81R12, 81R15, 81Q05, 81Q80, 81Q50

Received: 17.03.2019
Accepted: 14.06.2019

DOI: 10.20537/nd190207

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