Invariant polynomial
From Wikipedia, the free encyclopedia
In mathematics, an invariant polynomial is a polynomial P that is invariant under a group Γ acting on a vector space V. Therefore P is a Γ-invariant polynomial if
- P(γx) = P(x)
for all 
and 
.
Cases of particular importance are for Γ a finite group (in the theory of Molien series, in particular), a compact group, a Lie group or algebraic group. For a basis-independent definition of 'polynomial' nothing is lost by referring to the symmetric powers of the given linear representation of Γ.
[edit] References
- This article incorporates material from Invariant polynomial on PlanetMath, which is licensed under the GFDL.
