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Bott-Samelson Varieties and Configuration Spaces

alg-geom 2008-02-03 v1 代数几何

摘要

We give a new construction of the Bott-Samelson variety ZZ as the closure of a BB-orbit in a product of flag varieties (G/B)l(G/B)^l. This also gives an embedding of the projective coordinate ring of the variety into the function ring of a Borel subgroup: \CC[Z]\CC[B]\CC[Z] \subset \CC[B]. In the case of the general linear group G=GL(n)G = GL(n), this identifies ZZ as a configuration variety of multiple flags subject to certain inclusion conditions, closely related to the the matrix factorizations of Berenstein, Fomin and Zelevinsky. As an application, we give a geometric proof of the theorem of Kraskiewicz and Pragacz that Schubert polynomials are characters of Schubert modules. Our work leads on the one hand to a Demazure character formula for Schubert polynomials and other generalized Schur functions, and on the other hand to a Standard Monomial Theory for Bott-Samelson varieties.

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引用

@article{arxiv.alg-geom/9611019,
  title  = {Bott-Samelson Varieties and Configuration Spaces},
  author = {Peter M. Magyar},
  journal= {arXiv preprint arXiv:alg-geom/9611019},
  year   = {2008}
}

备注

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