The representation theory of the exceptional Lie superalgebras F(4) and G(3)

This paper is a resolution of three related problems proposed by Yu. I. Manin and V. Kac for the so-called {\it{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 {\it{superanalogue}} of Borel-Weil-Bott theorem.