The AKS Theorem, A.C.I. Systems and 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.

Topical Review (special volume 50 years Toda Lattice), with typos corrected and some additional references

References in corpus (6)

• Level-Spacing Distributions and the Airy Kernel
• Level-Spacing Distributions and the Bessel Kernel
• Level-Spacing Distributions and the Airy Kernel
• Matrices coupled in a chain. I. Eigenvalue correlations
• Lattices of matrices (revised)
• The Pfaff lattice and skew-orthogonal polynomials

Cited by in corpus (2)

• Rank shift conditions and reductions of 2d-Toda theory
• Isospectral deformations, the spectrum of Jacobi matrices, infinite continued fraction and difference operators. Application to dynamics on infinite dimensional systems