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 Inozemtsev V. I. On the Structure of Zonal Spherical Functions on Symmetric Spaces of Negative Curvature of Type AII 2019, Vol. 15, no. 2, pp.  179-186 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 Citation: Inozemtsev V. I.,  On the Structure of Zonal Spherical Functions on Symmetric Spaces of Negative Curvature of Type AII, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 2, pp.  179-186 DOI:10.20537/nd190207