Hilbert-Weyl theorem

Theorem: Let Γ be a compact Lie group acting on V. Then there exists a finite Hilbert basis for the ring 𝒫(Γ) (the set of invariant polynomials). [GSS]


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]


In [HW] on page 274.


  • 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