Introduction to Prehomogeneous Vector Spaces
About this Title
Tatsuo Kimura, Institute of Mathematics, University of Tsukuba, Tsukuba, Japan. Translated by Makoto Nagura and Tsuyoshi Niitani
Publication: Translations of Mathematical Monographs
Publication Year: 2002; Volume 215
ISBNs: 978-0-8218-2767-3 (print); 978-1-4704-4640-6 (online)
MathSciNet review: MR1944442
MSC: Primary 11S90; Secondary 11M41, 20G05
This is the first introductory book on the theory of prehomogeneous vector spaces, introduced in the 1970s by Mikio Sato. The author was an early and important developer of the theory and continues to be active in the field.
This book explains the basic concepts of prehomogeneous vector spaces, the fundamental theorem, the zeta functions associated with prehomogeneous vector spaces and a classification theory of irreducible prehomogeneous vector spaces.
This book is written for students, and is appropriate for second-year graduate level and above. However, because it is self-contained, covering algebraic and analytic preliminaries in considerable detail, the content may in fact prove to be accessible to many advanced undergraduate and beginning graduate students. It also provides a useful introduction for working mathematicians who want to learn about prehomogeneous vector spaces.
This book is most appropriate for second-year graduate students and above, but may be accessible to advanced undergraduate or beginning graduate students; it is also useful to working mathematicians who want to learn about prehomogeneous vector spaces.
Table of Contents
- Algebraic preliminaries
- Relative invariants of prehomogeneous vector spaces
- Analytic preliminaries
- The fundamental theorem of prehomogeneous vector spaces
- The zeta functions of prehomogeneous vector spaces
- Convergence of zeta functions of prehomogeneous vector spaces
- Classification of prehomogeneous vector spaces