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

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.