UC Berkeley

This thesis is a resolution of three related problems proposed by Yu. I. Manin and V. Kac for the so-called exceptional Lie superalgebras F(4) and G(3). The first problem posed by Kac (1978) is the problem of finding character and superdimension formulae for the simple modules. The second problem posed by Kac (1978) is the problem of classifying all indecomposable representations. The third problem posed by Manin (1981) is the problem of constructing the superanalogue of Borel-Weil-Bott theorem.