Remarks on finiteW algebras

The property of some finiteW algebras to be the commutant of a particular subalgebra of a simple Lie algebraG is used to construct realizations ofG. WhenGso(4, 2), unitary representations of the conformal and Poincaré algebras are recognized in this approach, which can be compared to the usual induced representation technics. WhenGsp(2,R) orsp(4,R), the anyonic parameter can be seen as the eigenvalue of aW generator in suchW representations ofG.Presented by P. Sorba at the 5th International Colloquium on Quantum Groups: Quantum Groups and Integrable Systems, Prague, 20–22 June 1996.P. Sorba would like to express his warm thanks to Professor estmír Burdík for the perfect organisation of the conference.