# invariant polynomial

An *invariant polynomial* is a polynomial $P$ that is invariant under a (compact) Lie group $\mathrm{\Gamma}$ acting on a vector space^{} $V$. Therefore $P$ is $\mathrm{\Gamma}$-invariant polynomial if $P(\gamma x)=P(x)$ for all $\gamma \in \mathrm{\Gamma}$ and $x\in V$.

## References

- GSS Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David: Singularities and Groups in Bifurcation Theory (Volume II). Springer-Verlag, New York, 1988.

Title | invariant polynomial |
---|---|

Canonical name | InvariantPolynomial |

Date of creation | 2013-03-22 13:40:19 |

Last modified on | 2013-03-22 13:40:19 |

Owner | Daume (40) |

Last modified by | Daume (40) |

Numerical id | 6 |

Author | Daume (40) |

Entry type | Definition |

Classification | msc 13A50 |