symmetric tensor

Let $V$ be a vector space over a field. Let $S_n$ be the symmetric group on$\{1,\mathrm{\dots },n\}$. An order-n tensor (http://planetmath.org/TensorProduct) $A\in V^{\otimes n}$ is said tobe if $P(\sigma )A=A$ for all $\sigma \in S_n$,where $P(\sigma )$ is the permutation operator associated to $\sigma$.The set of symmetric tensors in $V^{\otimes n}$ is denoted by$S^n(V)$.