On Ideal Generators for Affine Schubert Varieties

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We consider a certain class of Schubert varieties of the affine Grassmannian of type A. By embedding a Schubert variety into a finite-dimensional Grassmannian, we construct an explicit basis of sections of the basic line bundle by restricting certain Plücker co-ordinates. As a consequence, we write an explicit set of generators for the degree-one part of the ideal of the finite-dimensional embedding. This in turn gives a set of generators for the degree-one part of the ideal defining the affine Grassmannian inside the infinite Grassmannian which we conjecture to be a complete set of ideal generators. We apply our results to the orbit closures of nilpotent matrices. We describe (in a characteristic-free way) a filtration for the coordinate ring of a nilpotent orbit closure and state a conjecture on the SL(n)-module structures of the constituents of this filtration.
34 pages

Keywords

Algebraic Geometry, Commutative Algebra, Combinatorics, 14M15

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/73122

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0411127
 http://arxiv.org/abs/math/0411127

Collections

arXiv