Cotangent Bundle to the Flag Variety - I

TL;DR

This paper constructs a natural compactification of the cotangent bundle to the finite-dimensional flag variety within an affine Schubert variety, revealing new geometric structures related to Kac-Moody groups.

Contribution

It introduces a stable closed subset in an affine Schubert variety that compactifies the cotangent bundle of the flag variety, linking finite and infinite-dimensional geometric objects.

Findings

Identification of a stable closed subset in affine Schubert varieties

Construction of a compactification of the cotangent bundle

Connection between finite and infinite-dimensional flag varieties

Abstract

We show that there is a ${SL_n}$-stable closed subset of an affine Schubert variety in the infinite dimensional Flag variety (associated to the Kac-Moody group ${\widehat{SL_n}}$) which is a natural compactification of the cotangent bundle to the finite-dimensional Flag variety ${{SL_n/B}}$.