The AKS Theorem, A.C.I. Systems and Random Matrix Theory

TL;DR

This paper generalizes the Adler-Kostant-Symes Theorem and explores its applications in algebraic integrable systems and random matrix theory, bridging finite and infinite dimensional cases.

Contribution

It presents the most general form of the AKS Theorem and demonstrates its applications in both algebraic integrable systems and random matrix theory.

Findings

Generalized AKS Theorem applicable to finite and infinite dimensions

Derived algebraic completely integrable systems

Connected integrable systems with random matrix theory

Abstract

This paper gives the most general form of the Adler-Kostant-Symes Theorem, and many applications of it, both finite and infinite dimensional, the former yielding algebraic completely integrable (a.c.i.) systems, and the latter examples in random matrix theory.