Bulg. J. Phys. vol.36 no.3 (2009), pp. 147-169

Calogero-Moser Spaces and Representation Theory

E. Horozov1,2
1Department of Mathematics and Informatics, Sofia University, 5 J. Bourchier Blvd., Sofia 1126, Bulgaria
2Institute of Mathematics and Informatics, Bulg. Acad. of Sci., Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria
Abstract. We characterize the phase spaces of both rational and trigonometric Calogero-Moser systems in terms of certain infinite-dimensional Lie algebras. The two versions of these algebras are defined here together with some of their natural highest weight representations. The construction makes use of the theory of bispectral operators. All needed notions and results are described with details but most of the proofs are omitted. Our final result is that the Calogero-Moser spaces (in both cases) coincide with the orbit of the vacuum of reasonably defined group GL in this representation.

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