On quantization of affine Jacobi varieties of spectral curves

TL;DR

This paper explores the quantization of affine Jacobi varieties associated with spectral curves within a quantum integrable model related to $U_q(\hat{sl}(N))$, establishing commutation relations for the observables.

Contribution

It introduces a reduced model that enables the interpretation of the quantized affine Jacobi variety and derives its closed commutation relations.

Findings

Established a connection between quantum integrable models and affine Jacobi varieties.

Derived explicit commutation relations for the observables of the reduced model.

Provided a framework for understanding quantization in the context of spectral curves.

Abstract

A quantum integrable model related to $U_q(\hat{sl}(N))$ is considered. A reduced model is introduced which allows interpretation in terms of quantized affine Jacobi variety. Closed commutation relations for observables of reduced model are found.