Representations of Osp(2, 1) and the metaplectic representation

Abstract

Shift operator techniques are used to treat the irreducible representations of the superalgebra Osp(2, 1). Apart from obtaining the well known gradestar dispin representations which arise when the even part is the compact SU(2) algebra, the case when the star conditions on the even part are those satisfied by the noncompact SU(1, 1) algebra is also treated. In this case no gradestar representations arise, and the star representations are found to consist of the direct sum of two discrete series representations of SU(1, 1). One of these representations can be realized in terms of functions of a single complex variable, and turns out to be a simple example of a metaplectic representation.