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The trigonometric Grassmannian and a difference W-algebra

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Abstract

We introduce a W-algebra which is a central extension of the Lie algebra of difference operators with rational coefficients acting on functions of a discrete variable. We construct its natural fermionic and bosonic representations. We define a module over this difference W-algebra, which characterizes the trigonometric Calogero–Moser spaces.

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Authors and Affiliations

  1. Department of Mathematics, Université catholique de Louvain, Chemin du Cyclotron 2, 1348, Louvain-la-Neuve, Belgium

    Luc Haine

  2. Department of Mathematics and Informatics, Sofia University, 5 J. Bourchier Blvd., 1126, Sofia, Bulgaria

    Emil Horozov

  3. Institute of Mathematics and Informatics, Bulg. Acad. of Sci. Acad., G. Bonchev Str., Block 8, 1113, Sofia, Bulgaria

    Emil Horozov

  4. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

    Plamen Iliev

Authors
  1. Luc Haine
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  2. Emil Horozov
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  3. Plamen Iliev
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Correspondence to Luc Haine.

Additional information

*Supported in part by the Belgian Interuniversity Attraction Pole P06/02 and the European Science Foundation Program MISGAM.

**Partially supported by grant DO 01-257 of the NFSR of the Bulgarian Ministry of Education.

***Supported in part by NSF grant DMS-0901092.

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Haine, L., Horozov, E. & Iliev, P. The trigonometric Grassmannian and a difference W-algebra. Transformation Groups 15, 92–114 (2010). https://doi.org/10.1007/s00031-010-9077-6

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  • DOI: https://doi.org/10.1007/s00031-010-9077-6

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