Cusp Forms, Spanning Sets, and Super Symmetry: a New Geometric Approach to the Higher Rank and the Super Case

Automorphic and cusp forms on a complex bounded symmetric domain are a classical field of research in mathematics with fundamental applications to representation and number theory. Also for physicists they are of interest since the space of cusp forms is a quantization space of the underlying symmetric domain treated as a phase space. Aim of this book is to present a theory of super automorphic forms and a new geometric approach based on the frame flow of the underlying bounded symmetric domain constructing spanning sets for the space of cusp forms on symmetric domains of higher rank resp. on symmetric super domains. For this reason a general introduction to the geometry of complex bounded symmetric domains and to super structures is also included. In particular we present a new concept of 'parametrization' with far reaching applications within the theory of super manifolds and indispensable to a proper notion of super automorphic forms. The book, which has been developped from the author's PhD thesis, will fascinate every person generally interested in geometric quantization and in super structures, for young researchers it will be a great help.