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 .[1]

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.[2]

  1. ^ "invariant polynomial in nLab". ncatlab.org.
  2. ^ Draisma, Jan; Gijswijt, Dion. "Invariant Theory with Applications" (PDF).