Generalized Drinfeld-Sokolov Hierarchies and W-Algebras

Abstract

We review the construction of Drinfeld-Sokolov type hierarchies and classical W-algebras in a Hamiltonian symmetry reduction framework. We describe the list of graded regular elements in the Heisenberg subalgebras of the nontwisted loop algebra based on $g{l}_n$ and deal with the associated hierarchies. We exhibit an $s{l}_2$ embedding for each reduction of a Kac-Moody Poisson bracket algebra to a W-algebra of gauge invariant differential polynomials.

12 pages, (To appear in proc. of the NSERC-CAP Workshop on Quantum Groups, Integrable Models and Statistical Systems, Kingston, Canada, July 13-17 1992.)