Abstract
The space of functions A over the phase space of KdV-hierarchy is studied as a module over the ring \({\mathcal {D}}\) generated by commuting derivations. A \({\mathcal{D}}\) -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 \({\mathcal {D}}\) -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 between the two constructions is given.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Nakayashiki, A. On the Space of KdV Fields. Lett Math Phys 89, 85–100 (2009). https://doi.org/10.1007/s11005-009-0326-3
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DOI: https://doi.org/10.1007/s11005-009-0326-3