Orthosymplectic representations of Lie superalgebras (Q1097955)

The main result of this paper is that each self-contragredient finite- dimensional irreducible representation, \(\rho\), of a Lie superalgebra is orthosymplectic. That is, if there exists a nondegenerate even \(\rho\)- invariant bilinear form it is either supersymmetric or skew- supersymmetric. It is further shown that all finite-dimensional irreducible representations of the basic classical Lie superalgebras B(m,n), D(2k,n), D(2,1;\(\alpha)\), F(4) and G(3) are orthosymplectic. The author specifies all those irreducible representations of \(D(2k+1,n)\) and those typical irreducible representations of A(m,n) and C(n) which are orthosymplectic, leaving unsolved the atypical case. The relevance of the results to the determination of sub-superalgebras is pointed out.