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

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

Author(s): Inozemtsev V. I.

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

Download File
PDF, 364.18 Kb

This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License