BottSamelson Varieties and Configuration Spaces
Abstract
We give a new construction of the BottSamelson variety $Z$ as the closure of a $B$orbit in a product of flag varieties $(G/B)^l$. This also gives an embedding of the projective coordinate ring of the variety into the function ring of a Borel subgroup: $\CC[Z] \subset \CC[B]$. In the case of the general linear group $G = GL(n)$, this identifies $Z$ 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 BottSamelson varieties.
 Publication:

arXiv eprints
 Pub Date:
 November 1996
 arXiv:
 arXiv:alggeom/9611019
 Bibcode:
 1996alg.geom.11019M
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 email address pmagyar@lynx.neu.edu LaTeX