Generalization of a result of Matsuo and Cherednik to the Calogero-Sutherland- Moser integrable models with exchange terms

TL;DR

This paper extends the connection between solutions of generalized KZ equations and wave functions to a broader class of Calogero-Sutherland-Moser models with exchange terms, including spin and delta-function interactions.

Contribution

It generalizes Matsuo and Cherednik's result by constructing wave functions with arbitrary permutational symmetry for new integrable models with exchange terms.

Findings

Constructed wave functions with specified permutational symmetry.

Extended the link between KZ solutions and integrable models.

Included models with spin and delta-function interactions.

Abstract

A few years ago, Matsuo and Cherednik proved that from some solutions of the Knizhnik-Zamolodchikov (KZ) equations, which first appeared in conformal field theory, one can obtain wave functions for the Calogero integrable system. In the present communication, it is shown that from some solutions of generalized KZ equations, one can construct wave functions, characterized by any given permutational symmetry, for some Calogero-Sutherland-Moser integrable models with exchange terms. Such models include the spin generalizations of the original Calogero and Sutherland ones, as well as that with $\delta$-function interaction.