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In this paper, we construct finite dimensional irreducible representationsfor two different versions of \Z2 graded $osp(1|2)$ algebra based on eight- andten-generators. We find that there are two different second-order Casimiroperators for the ten generators version of the algebra one corresponding tothe $(0,0)$ sector and another in the $(1,1)$ sector. Consequently, it is shownthat the eight-generator version of the algebra has only one Casimir invariantin the $(0,0)$ sector. We present the differential operator realizations ofthese algebras. Starting with the highest weight, we construct the states ofthe irreducible finite-dimensional representations for both versions of thealgebras. The matrix realizations of the generators on the representation spacecorresponding to these states are written down explicitly.

The $osp(1|2)$ \Z2 graded algebra and its irreducible representations