Straightening for Standard Monomials on Schubert Varieties
نویسندگان
چکیده
w x Hodge and Pedoe 5 constructed bases of the homogeneous coordinate rings of the Schubert varieties in the Grassmannian, consisting of certain products of Plucker coordinates called standard monomials. Lakshmibai, ̈ w x Musili, and Seshadri 6 have generalized this theory extensively, giving standard monomial bases of the spaces of global sections of certain line bundles over unions of Schubert varieties in GrB where G is a classical group and B is a Borel subgroup. The purpose of this article is to give an elementary proof that the standard monomials yield a basis of the coordiŽ nate ring of a single Schubert subvariety of the flag variety that is, G is of . type A . The part of the original proof that is not elementary is the
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