- The relative frame bundle of an infinite-dimensional flag variety and solutions of integrable hierarchies
- Theoretical and Mathematical Physics
- Volume | Issue number
- 165 | 3
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
We develop a group theory approach for constructing solutions of integrable hierarchies corresponding to the deformation of a collection of commuting directions inside the Lie algebra of upper-triangular ZxZ matrices. Depending on the choice of the set of commuting directions, the homogeneous space from which these solutions are constructed is the relative frame bundle of an infinite-dimensional flag variety or the infinite-dimensional flag variety itself. We give the evolution equations for the perturbations of the basic directions in the Lax form, and they reduce to a tower of differential and difference equations for the coefficients of these perturbed matrices. The Lax equations follow from the linearization of the hierarchy and require introducing a proper analogue of the Baker—Akhiezer function.
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- Also published in Russian: Helminck, G.F., Helminck, A.G. & Opimakh, A.V. (2010). Относительное расслоение реперов бесконечномерного многообразия флагов и решения интегрируемых иерархий. --- Teoreticeskaja i matematiceskaja fizika, 165 --- (3), 440-471.
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