Comparison of quiver varieties, loop Grassmannians and nilpotent cones in type A

In type A we find equivalences of geometries arising in three settings: Nakajima's (framed) quiver varieties, conjugacy classes of matrices and loop Grassmannians. These are all given by explicit formulas. In particular, we embedd the framed quiver varieties into Beilinson-Drinfeld Grass-mannians. This provides a compactification of Nakajima varieties and a decomposition of affine Grassmannians into Nakajima varieties. As an application we provide a geometric version of symmetric and skew (GL(m), GL(n)) dualities.(c) 2022 Published by Elsevier Inc.

Automated summary

In type A, we identify the equivalences of geometries in three settings: Nakajima's (framed) quiver varieties, conjugacy classes of matrices, and loop Grassmannians. These equivalences are expressed through explicit formulas. In particular, we embed the framed quiver varieties into Beilinson-Drinfeld Grassmannians, leading to a compactification of Nakajima varieties and a decomposition of affine Grassmannians into Nakajima varieties. As an application, we present a geometric interpretation of symmetric and skew (GL(m), GL(n)) dualities.