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A Family of Irreducible Representations of the Witt Lie Algebra with Infinite-Dimensional Weight Spaces

Published online by Cambridge University Press:  04 December 2007

Charles H. Conley  and
Christiane Martin
Charles H. Conley
Affiliation:
Department of Mathematics, University of North Texas, Denton, TX 76203, U.S.A. E-mail: [email protected]
Christiane Martin
Affiliation:
Laboratoire de Mathématique-Physique, Université de Bourgogne, 9 Avenue Alain Savary, BP 400, 21011 Dijon, France
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Abstract

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We define a 4-parameter family of generically irreducible and inequivalent representations of the Witt Lie algebra on which the infinitesimal rotation operator acts semisimply with infinite-dimensional eigenspaces. They are deformations of the (generically indecomposable) representations on spaces of polynomial differential operators between two spaces of tensor densities on S1, which are constructed by composing each such differential operator with the action of a rotation by a fixed angle.

Keywords

Virasororepresentationdeformationdifferential operators
Type
Research Article
Information
Compositio Mathematica , Volume 128 , Issue 2 , September 2001 , pp. 153 - 176
Copyright
© 2001 Kluwer Academic Publishers