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Journal of Lie Theory 18 (2008), No. 4, 839--849
Copyright Heldermann Verlag 2008

Covariants and the No-Name Lemma

Mátyás Domokos
Rényi Institute of Mathematics, Hungarian Academy of Sciences, P. O. Box 127, 1364 Budapest, Hungary

A close connection between the no-name lemma (concerning algebraic groups acting on vector bundles) and the existence of sufficiently many independent rational covariants is pointed out. In particular, this leads to a new natural proof of the no-name lemma. For linearly reductive groups, the approach has a refined variant based on integral covariants. This yields a version of the no-name lemma that has a constructive nature.

Keywords: Rationality of fields of invariants, covariants, linearly reductive groups, Speiser's lemma.

MSC: 13A50, 14L30, 14E08

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