Bott-Samelson Varieties and Configuration Spaces
摘要
We give a new construction of the Bott-Samelson variety as the closure of a -orbit in a product of flag varieties . This also gives an embedding of the projective coordinate ring of the variety into the function ring of a Borel subgroup: . In the case of the general linear group , this identifies 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.
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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