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Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem

Bakalov, B.Horozov, E.Yakimov, M. — 1997

Serdica Mathematical Journal

This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral operators...

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