 
Summary: Journal of Pure and Applied Algebra 93 (1994) 135146
NorthHolland
135
Determining summands in
tensor products of Lie algebra
representations
Helmer Aslaksen*
Department of Mathematics, National University of Singapore, Singapore 0511, Singapore
Communicated by CA. Weibel
Received 28 September 1991
Revised 15 June 1992
Abstract
Aslaksen, H., Determining summands in tensor products of Lie algebra representations, Journal of
Pure and Applied Algebra 93 (1994) 135146.
We give some results that enable us to find certain summands in tensor products of Lie algebra
representations. We concentrate on the splitting of tensor squares into their symmetric and
antisymmetric parts. Our results are valid for any Lie algebra of arbitrary rank, but we do not
attempt to give the complete decomposition.
1. Introduction
The problem of decomposing tensor products of finitedimensional representations
