Role of the orthogonal group in construction of osp(1|2n) representations

Abstract

It is well known that the symmetric group has an important role (via Young tableaux formalism) both in labelling of the representations of the unitary group and in construction of the corresponding basis vectors (in the tensor product of the defining representations). We show that orthogonal group has a very similar role in the context of positive energy representations of osp(1|2n,R). In the language of parabose algebra, we essentially solve the long standing problem of reducibility of Green's ansatz representations.