DECOMPOSITION OF THE ENVELOPING ALGEBRA OF SL3

The adjoint representation of script s signℓ3 on its universal enveloping algebra script U sign is explicitly decomposed. The result is expressed as a presentation by generators and relations of the commutant in script U sign of the raising operators in script s signℓ3. Application is made to the analysis of the representations End(W) for finite-dimensional simple W. © 1990 American Institute of Physics.