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In mathematics, a representation on coordi … In mathematics, a representation on coordinate rings is a representation of a group on coordinate rings of affine varieties. Let X be an affine algebraic variety over an algebraically closed field k of characteristic zero with the action of a reductive algebraic group G. G then acts on the coordinate ring of X as a left regular representation: . This is a representation of G on the coordinate ring of X. The most basic case is when X is an affine space (that is, X is a finite-dimensional representation of G) and the coordinate ring is a polynomial ring. The most important case is when X is a symmetric variety; i.e., the quotient of G by a fixed-point subgroup of an involution.y a fixed-point subgroup of an involution.
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| rdfs:comment |
In mathematics, a representation on coordi … In mathematics, a representation on coordinate rings is a representation of a group on coordinate rings of affine varieties. Let X be an affine algebraic variety over an algebraically closed field k of characteristic zero with the action of a reductive algebraic group G. G then acts on the coordinate ring of X as a left regular representation: . This is a representation of G on the coordinate ring of X.entation of G on the coordinate ring of X.
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Representation on coordinate rings
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