On classical invariant theory and binary cubics

Gerald W. Schwarz

Annales de l'institut Fourier (1987)

  • Volume: 37, Issue: 3, page 191-216
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Schwarz, Gerald W.. "On classical invariant theory and binary cubics." Annales de l'institut Fourier 37.3 (1987): 191-216. <http://eudml.org/doc/74763>.

@article{Schwarz1987,
abstract = {Let $G$ be a reductive complex algebraic group, and let $C[mV]^G$ 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 $C[mV]^G$ can be obtained from those of $C[nV]^G$ by polarization and restitution for all $m&gt;n$. We bound and the degrees of generators and relations of $C[nV]^G$, extending results of Vust. We apply our techniques to compute the invariant theory of binary cubics.},
author = {Schwarz, Gerald W.},
journal = {Annales de l'institut Fourier},
keywords = {reductive complex algebraic group; algebra of invariant polynomial functions; invariant theory of binary cubics},
language = {eng},
number = {3},
pages = {191-216},
publisher = {Association des Annales de l'Institut Fourier},
title = {On classical invariant theory and binary cubics},
url = {http://eudml.org/doc/74763},
volume = {37},
year = {1987},
}

TY - JOUR
AU - Schwarz, Gerald W.
TI - On classical invariant theory and binary cubics
JO - Annales de l'institut Fourier
PY - 1987
PB - Association des Annales de l'Institut Fourier
VL - 37
IS - 3
SP - 191
EP - 216
AB - Let $G$ be a reductive complex algebraic group, and let $C[mV]^G$ 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 $C[mV]^G$ can be obtained from those of $C[nV]^G$ by polarization and restitution for all $m&gt;n$. We bound and the degrees of generators and relations of $C[nV]^G$, extending results of Vust. We apply our techniques to compute the invariant theory of binary cubics.
LA - eng
KW - reductive complex algebraic group; algebra of invariant polynomial functions; invariant theory of binary cubics
UR - http://eudml.org/doc/74763
ER -

References

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