Let $(V,\rho)$ be a representation of the group $G$. The $n$th symmetric power of $V_1$ and $V_2$ is a representation of $G$ over the symmetric power of vector spaces $\text{Sym}^n(V)$ under the linear transformation $\rho:G\to \text{Sym}^n(V)$ such that \(\rho(g)(v_1\odot v_2\odot \cdots \odot v_n) = (\rho(g)v_1\odot \rho(g)v_2\odot\cdots\odot\rho(g)v_n).\)
Wikidata ID: Q55643402