Infinite-dimensional flag manifolds in integrable systems. (English) Zbl 0838.22008
The authors present several instances where infinite-dimensional flag varieties and their holomorphic line bundles play a role in integrable systems. They describe the correspondence between flag varieties and Darboux transformations for the KP hierarchy and the \(n\)th KdV hierarchy, construct solutions of the \(n\)th MKdV hierarchy from the space of periodic flags, give a geometric interpretation of the Miura transform, and prove how the group extension connected with these line bundles shows up at integrable deformations of linear systems on \(P^1(C)\).
Reviewer: C.Udrişte (Bucureşti)
MSC:
| 22E65 | Infinite-dimensional Lie groups and their Lie algebras: general properties |
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
| 35Q58 | Other completely integrable PDE (MSC2000) |
| 43A80 | Analysis on other specific Lie groups |
| 17B65 | Infinite-dimensional Lie (super)algebras |
Keywords:
flag varieties; line bundles; integrable systems; Darboux transformations; Miura transform; integrable deformations; linear systemsReferences:
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