Remarks on Finite W Algebras

Details Remarks on Finite W Algebras Remarks on Finite W Algebras

1996-12-06

arxiv.org/abs/hep-th/9612070v2

Czech.J.Phys. 46 (1996) 1165-1178

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 16 pages, references added

Scientific paper

10.1007/BF01690330

The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G=so(4,2), unitary representations of the conformal and Poincare algebras are recognized in this approach, which can be compared to the usual induced representation technique. When G=sp(2,R) or sp(4,R), the anyonic parameter can be seen as the eigenvalue of a W generator in such W representations of G. The generalization of such properties to the affine case is also discussed in the conclusion, where an alternative of the Wakimoto construction for sl(2) level k is briefly presented. This mini review is based on invited talks presented by P. Sorba at the ``Vth International Colloquium on Quantum Groups and Integrable Systems'', Prague (Czech Republic), June 1996; ``Extended and Quantum Algebras and their Applications to Physics'', Tianjin (China), August 1996; ``Selected Topics of Theoretical and Modern Mathematical Physics'', Tbilisi (Georgia), September 1996; to be published in the Proceedings.

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