W-algebras for non-abelian Toda systems

TL;DR

This paper constructs classical W-algebras for specific non-abelian Toda systems linked to Lie groups GL(2n,R) and Sp(n,R), detailing their Poisson brackets and symmetries.

Contribution

It introduces a new construction of classical W-algebras for non-abelian Toda systems using block matrix representations and characteristic integrals.

Findings

Derived Poisson brackets for the Hamiltonian systems.

Presented symmetry transformations generated by W-algebras.

Provided explicit matrix representations for Toda equations.

Abstract

We construct the classical W-algebras for some non-abelian Toda systems associated with the Lie groups GL(2n,R) and Sp(n,R). We start with the set of characteristic integrals and find the Poisson brackets for the corresponding Hamiltonian counterparts. The convenient block matrix representation for the Toda equations is used. The infinitesimal symmetry transformations generated by the elements of the W-algebras are presented.