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

被引：3
|
作者：
Mirkovic, Ivan [1 ]
Vybornov, Maxim [2 ]
Krylov, Vasily [3 ,4 ,5 ]
机构：
[1] Univ Massachusetts Amherst, Dept Math & Stat, Amherst, MA 01003 USA
[2] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA
[3] Natl Res Univ Higher Sch Econ, Moscow, Russia
[4] Dept Math, 6 Usacheva st, Moscow 119048, Russia
[5] Skolkovo Inst Sci & Technol, Moscow, Russia
来源：
ADVANCES IN MATHEMATICS | 2022年 / 407卷
基金：
美国国家科学基金会;
关键词：
Quivervarieties; LoopGrassmannians; Nilpotentcones; LAGRANGIAN CONSTRUCTION; REPRESENTATIONS; SINGULARITIES; INSTANTONS; SHEAVES;
D O I：
10.1016/j.aim.2022.108397
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页数：54
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