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

✍ Scribed by Takeyoshi Kogiso; Go Miyabe; Miyuki Kobayashi; Tatsuo Kimura

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 347 KB
• Volume: 251
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8607

✦ Synopsis

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 Sp n × GL 2 1 ⊗ 2 1 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 .  2002 Elsevier Science (USA)