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Introduction to Prehomogeneous Vector Spaces

Tatsuo Kimura

出版	American Mathematical Soc., 2003
主題	Mathematics / Algebra / LinearMathematics / Number TheoryMathematics / Vector Analysis
ISBN	08218276779780821827673
URL	http://books.google.com.hk/books?id=qYH8oIekZF4C&hl=&source=gbs_api
EBook	SAMPLE

註釋

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. The subject combines elements of several areas of mathematics, such as algebraic geometry, Lie groups, analysis, number theory, and invariant theory. An important objective is to create applications to number theory. For example, one of the key topics is that of zeta functions attached to prehomogeneous vector spaces; these are generalizations of the Riemann zeta function, a cornerstone of analytic number theory. Prehomogeneous vector spaces are also of use in representation theory, algebraic geometry and invariant theory. 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. It strives, and to a large extent succeeds, in making this content, which is by its nature fairly technical, self-contained and accessible. The first section of the book, "Overview of the theory and contents of this book," Is particularly noteworthy as an excellent introduction to the subject.