Exactly integrable systems connected to semisimple algebras of second rank A_2, B_2, C_2, G_2

TL;DR

This paper presents explicit forms of exactly integrable systems linked to second-rank semisimple algebras, providing general solutions via matrix elements of fundamental group representations.

Contribution

It introduces a unified explicit formulation of integrable systems associated with second-rank semisimple algebras for any grading, with solutions expressed through fundamental representations.

Findings

Explicit forms of integrable systems for second-rank semisimple algebras.

General solutions expressed via matrix elements of fundamental representations.

Applicable to arbitrary grading choices.

Abstract

Exactly integrable systems connected to semisimple algebras of second rank with an arbitrary choice of grading are presented in explicit form. General solutions of these systems are expressed in terms of matrix elements of two fundamental representations of the corresponding semisimple groups.