On Ideal Generators for Affine Schubert Varieties

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dc.creatorKreiman, V.
dc.creatorLakshmibai, V.
dc.creatorMagyar, P.
dc.creatorWeyman, J.
dc.date2004-11-06
dc.date.accessioned2026-07-07T05:14:01Z
dc.date.available2026-07-07T05:14:01Z
dc.descriptionWe 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.
dc.description34 pages
dc.identifierhttps://arxiv.org/abs/math/0411127
dc.identifierhttp://arxiv.org/abs/math/0411127
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73122
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subjectCombinatorics
dc.subject14M15
dc.titleOn Ideal Generators for Affine Schubert Varieties
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