Igusa local zeta functions and parabolic castling transformation of prehomogeneous vector spaces
type: Item
instance of: scholarly article
title: Igusa local zeta functions and parabolic castling transformation of prehomogeneous vector spaces
zbMATH Open document ID: 0926.11060
author: Hiroshi Hosokawa
published in: Journal of Number Theory
publication date: 1999-12-02T00:00:00Z
review text: The castling transformation is a standard procedure for constructing new prehomogeneous vector spaces from a given one and plays a crucial role in the classification of prehomogeneous vector spaces. \textit{J. I. Igusa} [Am. J. Math. 110, 197-233 (1988; Zbl 0662.12014)] gives a relation between the Igusa local zeta function of a prehomogeneous vector space and the Igusa local zeta function of its castling transformation. \textit{Y. Teranishi} [Nagoya Math. 98, 139-156 (1985; Zbl 0573.20041)] gave a generalization of the castling transformation related to parabolic subgroups. In this paper, a relation between the Igusa local zeta function of a prehomogeneous vector space and the Igusa local zeta functions of its parabolic castling transformation is obtained.
reviewed by: Ranjeet Sehmi
Mathematics Subject Classification ID: 11M38
Mathematics Subject Classification ID: 11S90
Mathematics Subject Classification ID: 14G10
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 11S40
zbMATH DE Number: 1271771
zbMATH Keywords: castling transformation
zbMATH Keywords: prehomogeneous vector spaces
zbMATH Keywords: Igusa local zeta function
zbMATH Keywords: parabolic subgroups
MaRDI profile type: Publication
full work available at URL: jnth.1998.2311
OpenAlex ID: W2002849926
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DOI: 10.1006/JNTH.1998.2311
description: scientific article; zbMATH DE number 1271771