Fourth degree Casimir operator of the semisimple graded Lie algebra (Sp(2<i>N</i>); 2<i>N</i>)

Abstract

The Casimir operators of the graded Lie algebra (Sp(2N);2N) [denoted also by OSp(1/2N) in the literature] are discussed. A general method, according to which the higher degree Casimir operators of the graded Lie algebras, in our case of the (Sp(2N);2N), can be constructed is developed. It is shown that the third degree Casimir operator of this graded Lie algebra does not exist. The Casimir operator of the fourth degree is derived explicitly.