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

By B. Bakalov, E. Horozov and M. Yakimov


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 of rank and order two

Topics: Bispectral Operators, Darboux Transformations, W–Algebras, Highest Weight Representations, KP–Hierarchy
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Year: 1997
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