On quantum L-operator for two-dimensional lattice Toda model

TL;DR

This paper investigates the quantum lattice Toda model for type A Lie algebras, providing a second-order correction to its L-operator and proving the non-existence of third-order solutions.

Contribution

It introduces a second-order correction to the known L-operator and demonstrates the impossibility of third-order corrections for the model.

Findings

Second-order correction to the L-operator is derived.

Third-order correction equation has no solutions.

Enhances understanding of quantum lattice Toda models.

Abstract

The two-dimensional quantum lattice Toda model for the affine and simple Lie algebras of the type A is considered. For its known L-operator a correction of the second order in the lattice parameter is found. It is proved that the equation determining a correction of the third order has no solutions.