Lax operator algebras of type $G_2$

TL;DR

This paper constructs Lax operator algebras associated with the root system G_2 on finite genus Riemann surfaces using Tyurin data, expanding the algebraic framework for integrable systems.

Contribution

It introduces the construction of Lax operator algebras for the G_2 root system on Riemann surfaces with Tyurin data, a novel extension in the field.

Findings

Lax operator algebras for G_2 are explicitly constructed.

The framework applies to arbitrary finite genus Riemann surfaces.

Provides a foundation for further studies in integrable systems related to G_2.

Abstract

Lax operator algebras for the root system $G_2$, and arbitrary finite genus Riemann surfaces and Tyurin data on them are constructed.