Cotangent Bundle to the Flag Variety - II

2016/12/20 by V. Lakshmibai, Lakshmibai, Venkatramani, Rahul Kumar Singh +1
Mathematics · #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1612.06773

Abstract

Let P be a parabolic subgroup in SL_n(\mathbb C). We show that there is a SL_n(\mathbb C)-stable closed subvariety of an affine Schubert variety in an infinite dimensional partial Flag variety (associated to the Kac-Moody group \widehatSL_n(\mathbb C)) which is a natural compactification of the cotangent bundle to SL_n(\mathbb C)/P. As a consequence, we recover the Springer resolution for any orbit closure inside the variety of nilpotent matrices.

Related

• Cotangent bundle to the Grassmann variety
• The Cotangent Bundle of a Cominuscule Grassmannian
• Blow-up of a generalized flag variety
• Existence of affine pavings for varieties of partial flags associated to nilpotent elements
• Parabolic Kazhdan-Lusztig polynomials and Schubert varieties