Gauging of geometric actions and integrable hierarchies of the KP type (Q2747042)

The paper consists of two parts. In the first part the authors derive massive gauge-invariant generalisation of geometric actions on coadjoint orbits of an arbitrary infinite dimensional group \(G\), and show that there exists a generalised version of the zero-curvature representation for the equations of motion on the coadjoint orbit. The gauge group \(H\) here is an infinite-dimensional subgroup of \(G\). In the second part the authors study the special case in which \(G\) is the Kac-Moody group. In this case the equations of motion for the underlying gauge WZNW geometric action are identified with the additional symmetry flows of the generalised Drinfeld-Sokolov hierarchies. The case of loop groups \(\widehat{SL(N+R)}\) is treated in a considerable detail. In this case the hierarchies correspond to a class of constrained KP hierarchies. Loop algebras of additional symmetries and explicit derivation of the general Darboux-Bäcklund solutions of such constrained KP hierarchies are described.