b-Functions of the Prehomogeneous Vector Space Arising from a Cuspidal Character Sheaf of E7

The purpose of this paper is to compute the explicit form of the relative invariants and their b-functions of a certain important prehomogeneous vector space appearing in the study of a cuspidal character sheaf of the exceptional group E7. For every simple algebraic group excepting the type E7, the b-functions of this kind of prehomogeneous vector space have been determined.