Polynomial invariant
= Polynomial invariant
For a <group representation> on $V$, a polynomial invariant is a <polynomial> $p$ satisfying $p(gv)=p(v)$ for every $g\in G$. Homogeneous degree-$d$ invariants form $(\operatorname{Sym}^d V^*)^G$. Using the <symmetric power> matters: an alternating <invariant tensor> contracted with repeated copies of the same commuting vector can vanish.