Journal of Lie Theory

no. 4
Covariants and the No-Name Lemma
Journal of Lie Theory, Volume 18 (2008) no. 4, pp. 839-849
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.
DOI: 10.5802/jolt.528
Classification: 13A50, 14L30, 14E08
Keywords: Rationality of fields of invariants, covariants, linearly reductive groups, Speiser's lemma 
@article{JOLT_2008_18_4_a5,
     author = {M. Domokos},
     title = {Covariants and the {No-Name} {Lemma}},
     journal = {Journal of Lie Theory},
     pages = {839--849},
     year = {2008},
     volume = {18},
     number = {4},
     doi = {10.5802/jolt.528},
     zbl = {1197.13008},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.528/}
}
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M. Domokos. Covariants and the No-Name Lemma. Journal of Lie Theory, Volume 18 (2008) no. 4, pp. 839-849. doi: 10.5802/jolt.528

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