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G L n -Invariant tensors and graphs

Martin Markl (2008)

Archivum Mathematicum

We describe a correspondence between GL n -invariant tensors and graphs. We then show how this correspondence accommodates various types of symmetries and orientations.

Invariants of four subspaces

Gerry W. Schwarz, David L. Wehlau (1998)

Annales de l'institut Fourier

We consider problems in invariant theory related to the classification of four vector subspaces of an n -dimensional complex vector space. We use castling techniques to quickly recover results of Howe and Huang on invariants. We further obtain information about principal isotropy groups, equidimensionality and the modules of covariants.

Le théorème fondamental des invariants pour les groupes finis

Mustapha Rais (1977)

Annales de l'institut Fourier

Soit V un espace vectoriel complexe de dimension finie. Soit G un sous-groupe fini de G L ( V ) . On montre que pour chaque entier p ≥ 1 , le corps des fonctions rationnelles invariantes par G sur V p s’obtient en prenant le corps des fractions de l’algèbre engendrée par les polarisées des fonctions polynômes G -invariantes sur V .

On classical invariant theory and binary cubics

Gerald W. Schwarz (1987)

Annales de l'institut Fourier

Let G be a reductive complex algebraic group, and let C [ m V ] G denote the algebra of invariant polynomial functions on the direct sum of m copies of the representations space V of G . There is a smallest integer n = n ( V ) such that generators and relations of C [ m V ] G can be obtained from those of C [ n V ] G by polarization and restitution for all m > n . We bound and the degrees of generators and relations of C [ n V ] G , extending results of Vust. We apply our techniques to compute the invariant theory of binary cubics.

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