Excitation Scattering in Integrable Models and Hall-Littlewood-Kerov Polynomials

Abstract

The S-matrices for the scattering of two excitations in the XYZ model and in all of its SU(n)-type generalizations are obtained from the asymptotic behavior of Kerov's generalized Hall-Littlewood polynomials. These physical scattering processes are all reduced to geometric s-wave scattering problems on certain quantum-symmetric spaces, whose zonal spherical functions these Hall-Littlewood-Kerov polynomials are. Mathematically, this involves a generalization with an unlimited number of parameters of the Macdonald polynomials. Physically, our results suggest that, of the (1+1)-dimensional models, the integrable ones are those, for which the scattering of excitations becomes geometric in the sense above.

12 pages, EFI 92-44

References in corpus (2)

• Macdonald Polynomials from Sklyanin Algebras: A Conceptual Basis for the $p$-Adics-Quantum Group Connection
• $Z_n$ Baxter Models and Quantum Symmetric Spaces

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