### Introduction to Prehomogeneous Vector Spaces

Abstract Let G be a connected reductive linear algebraic group and X a G-homogeneous affine algebraic variety both defined over a p-adic field k, where we assume a minimal k-parabolic subgroup of G acts with open orbit. Fingerprint Spherical Functions.

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Homogeneous Space. Functional equation.

Prehomogeneous Vector Spaces. Linear Algebraic Groups. P-adic Fields.

## Decomposition of reductive regular Prehomogeneous Vector Spaces

Parabolic Subgroup. Algebraic Variety.

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Riemann zeta function. Keywords p-adic homogeneous space prehomogeneous vector space Spherical function. This is the first introductory book on the theory of prehomogeneous vector spaces, introduced in the s 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.

## Introduction To Prehomogeneous Vector Spaces

It also provides a useful introduction for working mathematicians who want to learn about prehomogeneous vector spaces. See All Customer Reviews.

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