Rational covariants of reductive groups and homaloidal polynomials

Kraft, Hanspeter and Schwarz, Gerald W.. (2001) Rational covariants of reductive groups and homaloidal polynomials. Mathematical research letters, Vol. 8. pp. 641-650.

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Official URL: http://edoc.unibas.ch/dok/A5842776

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Let G be a complex reductive group, V a G-module and f a nonconstant homogenous invariant polynomial on V. We investigate relations between the following properties:- The differential df: V -< V* is dominant;- The invariant f is homaloidal, i.e., df induces a birational map P(V) -< P(V*);- V is a stable representation, i.e., the generic G-orbit in V is closed.If f generates the invariants, we show that the properties are equivalent, generalizing results of Sato-Kimura on prehomogeneous vector spaces.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Algebra (Kraft)
UniBasel Contributors:Kraft, Hanspeter
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:International Press
Note:Publication type according to Uni Basel Research Database: Journal article
edoc DOI:
Last Modified:31 Dec 2015 10:49
Deposited On:08 Jun 2012 06:47

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