The group with Grassmann structureUOSP(1.2)

Abstract

The finite-dimensional representations of the Lie superalgebraosp(1.2) and the group with Grassmann structureOSP(1.2) have been studied. The explicit expression of the projection operator of the superalgebraosp(1.2) has been found. The operator permits an arbitrary finite-dimensional representation to be expanded in the components multiple to the irreducible ones. The Clebsch-Gordan coefficients for the tensor product of two arbitrary irreducible representations have been obtained. The matrix elements of the irreducible representations of the groupUOSP(1.2) [the analoque of the compact form of the groupOSP(1.2)] are studied. The explicit form of these matrix elements, the differential equations satisfied by them, and the integral of their product have been found.