Symmetric power

• In linear algebra, the n-th symmetric power of a vector space V is the vector subspace of the symmetric algebra of V consisting of degree-n elements.
• In algebraic topology, the n-th symmetric power of a topological space X is the quotient space, as in the beginning of this article.
• In algebraic geometry, a symmetric power is defined in a way similar to that in algebraic topology. For example, if is an affine variety, then the GIT quotient is the n-th symmetric power of X.