A classification of lowest weight irreducible modules over Z22-graded extension of osp(1|2)

Abstract

We investigate representations of the Z22-graded extension of osp(1|2), which is the spectrum generating algebra of the recently introduced Z22-graded version of superconformal mechanics. The main result is a classification of irreducible lowest weight modules of the Z22-graded extension of osp(1|2). This is done via the introduction of Verma modules and its maximal invariant submodule generated by singular vectors. Explicit formulas of all singular vectors are also presented.