$Z_n$ Baxter Models and Quantum Symmetric Spaces

Abstract

The scattering of two excitations (both of the simplest kind) in the magnetic model related to the $Z_n$\--Baxter model is naturally described for $n\to \infty$ in terms of the Macdonald polynomials for root system $A_1$. These polynomials play the role of zonal spherical functions for a two parameter family of quantum symmetric spaces. These spaces ``interpolate'' between various $p$\--adic and real symmetric spaces.

15 pages

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