About: Symmetric power

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In mathematics, the n-th symmetric power of an object X is the quotient of the n-fold product by the permutation action of the symmetric group . More precisely, the notion exists at least in the following three areas:

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  • In mathematics, the n-th symmetric power of an object X is the quotient of the n-fold product by the permutation action of the symmetric group . More precisely, the notion exists at least in the following three areas: * 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 (here the product is a tensor product). * 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. (en)
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  • In mathematics, the n-th symmetric power of an object X is the quotient of the n-fold product by the permutation action of the symmetric group . More precisely, the notion exists at least in the following three areas: (en)
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  • Symmetric power (en)
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