 Symmetric power

The nth symmetric power $S^{n}V$ is the quotient of $V^{\otimes n}$ that identifies tensors differing by a permutation of their factors. Equivalently, over characteristic zero it is the subspace of symmetric tensors.

In mathematics, especially in the field of algebra and representation theory, symmetric power refers to a specific type of construction that takes a given vector space or a module and creates a new one by considering the symmetric tensors of the original space.