Dual Baxter equations and quantization of Affine Jacobian

TL;DR

This paper introduces a quantum integrable model that quantizes affine hyper-elliptic Jacobians and reveals a duality property linking eigen-functions of dual models through inverse Planck constants.

Contribution

It presents a novel quantum integrable model for affine hyper-elliptic Jacobians and demonstrates a duality between models with inverse Planck constants.

Findings

Existence of a dual quantum model with inverse Planck constant

Eigen-functions of dual models coincide

Duality relates homologies and cohomologies of quantized Jacobians

Abstract

A quantum integrable model is considered which describes a quantization of affine hyper-elliptic Jacobian. This model is shown to possess the property of duality: a dual model with inverse Planck constant exists such that the eigen-functions of its Hamiltonians coincide with the eigen-functions of Hamiltonians of the original model. We explain that this duality can be considered as duality between homologies and cohomologies of quantized affine hyper-elliptic Jacobian.