Calogero-Moser spaces and an adelic $W$-algebra

Horozov, Emil

Annales de l'Institut Fourier, Tome 55 (2005) no. 6, pp. 2069-2090.

Nous construisons une algèbre nommée adélique $W$-algèbre puis, nous construisons une représentation bosonique naturelle. Nous montrons ensuite que les points des espaces de Calogero-Moser sont en correspondance biunivoque avec les fonctions tau en cette représentation.

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.

Classification : 37K30, 37K35
Keywords: Fock spaces, bispectral operators, Sato's theory for KP hierarchy
Mot clés : espaces de Fock, opérateurs bispectraux, théorie de Sato de KP-hiérarchie

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