# Hilbert-Weyl theorem

Theorem: Let $\mathrm{\Gamma}$ be a compact Lie group acting on $V$. Then there exists a finite Hilbert basis for the ring $\mathcal{P}(\mathrm{\Gamma})$ (the set of invariant polynomials). [GSS]

proof:

In [GSS] on page 54.

Theorem:(as stated by Hermann Weyl)

The (absolute) invariants corresponding to a given set of representations of a finite or a compact Lie group have a finite integrity basis. [HW]

proof:

In [HW] on page 274.

## References

- GSS Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David.: Singularities and Groups in Bifurcation Theory (Volume II). Springer-Verlag, New York, 1988.
- HW Hermann, Weyl: The Classical Groups: Their Invariants and Representations. Princeton University Press, New Jersey, 1946.

Title | Hilbert-Weyl theorem |
---|---|

Canonical name | HilbertWeylTheorem |

Date of creation | 2013-03-22 13:39:54 |

Last modified on | 2013-03-22 13:39:54 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 9 |

Author | mathcam (2727) |

Entry type | Theorem |

Classification | msc 22E20 |