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b-Functions of Prehomogeneous Vector Spaces of Dynkin–Kostant Type for Exceptional Groups

Published online by Cambridge University Press:  04 December 2007

Kimitoshid Ukai
Kimitoshid Ukai
Affiliation:
Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan.e-mail: k_ukai@hkg.odn.ne.jp
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Abstract

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The purpose of this paper is to determine the b-functions of all the prehomogeneous vector spaces associated to nilpotent orbits in the Dynkin–Kostant theory for all the complex simple algebraic groups of exceptional type. Our method to calculate b-functions is based on the structure theorem for b-functions of several variables and the functional equations for them.

Keywords

b-functionsprehomogeneous vector spacesnilpotent orbits
Type
Research Article
Information
Compositio Mathematica , Volume 135 , Issue 1 , January 2003 , pp. 49 - 102
Copyright
© 2003 Kluwer Academic Publishers