Theory of prehomogeneous vector spaces (algebraic part)—the English translation of Sato’s lecture from Shintani’s note
- 1 December 1990
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 120, 1-34
- https://doi.org/10.1017/s0027763000003214
Abstract
The purpose of this paper is to introduce a-functions and b-functions of prehomogeneous vector spaces in the original way of M. Sato and give a proof of the structure theorem of them. All the results were obtained by M. Sato when he constructed the theory of prehomogeneous vector spaces in 60’s. However he did not write a paper on his outcomes at that time. His theory was distributed through his lectures and informal seminars. Only small number of people could know it. The only publication left for us is a mimeographed note of his lecture [Sa-Sh1] written by T. Shintani in Japanese.Keywords
This publication has 4 references indexed in Scilit:
- $q$-analogue of de Rham cohomology associated with Jackson integrals, IProceedings of the Japan Academy, Series A, Mathematical Sciences, 1990
- Micro-local analysis of prehomogeneous vector spacesInventiones Mathematicae, 1980
- A classification of irreducible prehomogeneous vector spaces and their relative invariantsNagoya Mathematical Journal, 1977
- On Zeta Functions Associated with Prehomogeneous Vector SpacesAnnals of Mathematics, 1974