Cotangent Bundle to the Flag Variety - II
Venkatramani Lakshmibai, Rahul Singh

TL;DR
This paper constructs a natural compactification of the cotangent bundle to flag varieties using affine Schubert varieties, providing a new geometric perspective and recovering the Springer resolution for nilpotent orbit closures.
Contribution
It introduces a novel compactification of cotangent bundles to flag varieties via affine Schubert varieties within an infinite-dimensional Kac-Moody setting.
Findings
Constructs a $SL_n(C)$-stable closed subvariety in an affine Schubert variety.
Provides a geometric realization of the cotangent bundle compactification.
Recovers the Springer resolution for nilpotent orbit closures.
Abstract
Let be a parabolic subgroup in . We show that there is a -stable closed subvariety of an affine Schubert variety in an infinite dimensional partial Flag variety (associated to the Kac-Moody group ) which is a natural compactification of the cotangent bundle to . As a consequence, we recover the Springer resolution for any orbit closure inside the variety of nilpotent matrices.
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Taxonomy
TopicsMathematics and Applications
