Nonregular 2-Simple Prehomogeneous Vector Spaces of Type I and Their Relative Invariants

After the fundamental theorem for nonregular reductive prehomogeneous vector spaces was proved by A. Gyoja (Tsukuba J. Math.14 (1990), 437–457), the construction of the theory of nonregular prehomogeneous vector spaces became an interesting problem. However, only (Spn × GL2, Λ1 2Λ1, M(2n, 3)) is known as an interesting example of nonregular reductive prehomogeneous vector spaces. In this paper, we give some other interesting examples by constructing all relative invariants of nonregular 2-simple prehomogeneous vector spaces of type I. We consider everything over the complex number field .