GROUP-THEORETICAL STRUCTURE OF N=1 AND N=2 2-FORM SUPERGRAVITY

We clarify the group-theoretical structure of N=1 and N=2 two-form sup ergravity, which is classically equivalent to the Einstein supergravit y. N=1 and N=2 two-form supergravity theories can be formulated as gau ge theories. By introducing two Grassmann variables theta(A) (A=1,2), we construct the explicit representations of the generators Q(i) of th e-gauge group, which makes it possible to express any product of the g enerators as a linear combination of the generators Q(i)Q(j)=Sigma(k)f (k)(ij)Q(k). By using the expression and the tensor product representa tion, we show how to construct finite-dimensional representations of t he gauge groups. Based on these representations, we construct the Lagr angians of N=1 and N=2 two-form supergravity theories.