Invariant polynomial
In mathematics, an invariant polynomial is a polynomial that is invariant under a group acting on a vector space. Therefore, is a -invariant polynomial if
for all and.
Cases of particular importance are for Γ a finite group, 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.
