Quotients of some prehomogeneous vector spaces
type: Item
instance of: scholarly article
title: Quotients of some prehomogeneous vector spaces
zbMATH Open document ID: 0893.17007
author: Hiroyuki Ochiai
published in: Journal of Algebra
publication date: 1998-05-02T00:00:00Z
review text: This paper gives a ``reduction'' of prehomogeneous vector spaces over an algebraically closed field \(\mathbb{C}\) and its application to the construction of relative invariants. Let \((G\times H,\rho,V)\) be a prehomogeneous vector space where \(G\times H\) is a product of two algebraic groups. If \(V//G:=\text{Spec}(\mathbb{C}[V]^G)\) is a vector space and if the action \(\overline\rho\) of \(H\) on \(V//G\) is prehomogeneous, then the properties of \((G\times H,\rho,V)\) are expected to be obtained from those of the prehomogeneous vector space \((H,\overline\rho,V//G)\). The author of this paper carried out the construction of the relative invariants of the prehomogeneous vector spaces \((\text{SL}_5\times\text{GL}_3,\Lambda_2\otimes\Lambda_1)\) and \((\text{Spin}_{10}\times\text{GL}_3\), half-spin rep. \(\otimes\Lambda_1)\).
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 1026082
zbMATH Keywords: prehomogeneous vector spaces
zbMATH Keywords: construction of relative invariants
reviewed by: Masakazu Muro
MaRDI profile type: Publication
OpenAlex ID: W2033972332
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DOI: 10.1006/JABR.1996.6979
description: scientific article; zbMATH DE number 1026082