Infinite-dimensional flag manifolds in integrable systems

Abstract

Abstract. In this paper we present several instances where infinite dimensional flag varieties and their holomorphic line bundles play a role in integrable systems. As such, we give the correspondance between flag varieties and Darboux transformations for the K P-hierarchy and the n-th KdV-hierarchy. We construct solutions of the n-th M KdVhierarchy from the space of periodic flags and we treat the geometric interpretation of the Miura transform. Finally we show how the group extension connected with these line bundles shows up at integrable deformations of linear systems on ‫ސ‬ 1 ‫.)ރ(‬