Invariant polynomial

In mathematics, an invariant polynomial is a polynomial $P$ that is invariant under a group $\Gamma$ acting on a vector space $V$ . Therefore $P$ is a $\Gamma$ -invariant polynomial if

for all $\gamma \in \Gamma$ and $x \in V$ .

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.

单词	Invariant polynomial
释义	Invariant polynomial 英语百科 Invariant polynomial In mathematics, an invariant polynomial is a polynomial $P$ that is invariant under a group $\Gamma$ acting on a vector space $V$ . Therefore $P$ is a $\Gamma$ -invariant polynomial if for all $\gamma \in \Gamma$ and $x \in V$ . 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.
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