Cotangent bundle to the Grassmann variety
V. Lakshmibai
TL;DR
This paper constructs an affine Schubert variety within an infinite-dimensional flag variety that serves as a natural compactification of the cotangent bundle to the Grassmannian, linking geometric representation theory and algebraic geometry.
Contribution
It introduces a new affine Schubert variety that compactifies the cotangent bundle to the Grassmannian, expanding understanding of geometric structures in Kac-Moody groups.
Findings
Affine Schubert variety acts as a compactification of the cotangent bundle.
Connects infinite-dimensional flag varieties with classical geometric objects.
Provides a new perspective on the geometry of Grassmannians.
Abstract
We show that there is an affine Schubert variety in the infinite dimensional partial Flag variety (associated to the two- step parabolic subgroup of the Kac-Moody group {\hat SL(n)}, corresponding to omitting {\alpha}_0,{\alpha}_d) which is a natural compactification of the cotangent bundle to the Grassmann variety.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons