Displaying similar documents to “Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem”

Backlund-Darboux Transformations in Sato's Grassmannian

Bakalov, B., Horozov, E., Yakimov, M. (1996)

Serdica Mathematical Journal

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We define Bäcklund–Darboux transformations in Sato’s Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the action of these transformations on related objects: wave functions, tau-functions and spectral algebras.

Calogero-Moser spaces and an adelic W -algebra

Emil Horozov (2005)

Annales de l’institut Fourier

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We introduce a Lie algebra, which we call adelic W -algebra. Then we construct a natural bosonic representation and show that the points of the Calogero-Moser spaces are in 1:1 correspondence with the tau-functions in this representation.

Compact AC-operators

Ian Doust, Byron Walden (1996)

Studia Mathematica

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We prove that compact AC-operators have a representation as a combination of disjoint projections which mirrors that for compact normal operators. We also show that unlike arbitrary AC-operators, compact AC-operators admit a unique splitting into real and imaginary parts, and that these parts must necessarily be compact.

Dunkl operators

G. J. Heckman (1996-1997)

Séminaire Bourbaki

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