On the Space of KdV Fields

Details On the Space of KdV Fields On the Space of KdV Fields

2009-04-03

arxiv.org/abs/0904.0501v1

Physics

Mathematical Physics

13 pages

Scientific paper

The space of functions A over the phase space of KdV-hierarchy is studied as a module over the ring D generated by commuting derivations. A D-free resolution of A is constructed by Babelon, Bernard and Smirnov by taking the classical limit of the construction in quantum integrable models assuming a certain conjecture. We propose another D-free resolution of A by extending the construction in the classical finite dimensional integrable system associated with a certain family of hyperelliptic curves to infinite dimension assuming a similar conjecture. The relation of two constructions is given.

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