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Algebraic Geometry And Representation Theory

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2 domain-specific abstractions whose origin domain is Algebraic Geometry And Representation Theory.

  • Representation on coordinate rings — A group action on an affine algebraic variety induces a contragredient linear action on its coordinate ring by precomposing regular functions with the inverse geometric action.
  • Standard monomial theory — A method constructing explicit bases for coordinate rings and line-bundle sections on flag and Schubert varieties through ordered products satisfying straightening relations.