237 citations · 1.2k across the 58 of their papers we have counts for
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Instantons on ALE spaces for classical groups, involutions on quiver varieties, and quantum symmetric pairs
Hiraku Nakajima
Moduli spaces of instantons on ALE spaces for classical groups are examples of fixed point sets of involutions on quiver varieties, i.e., -quiver varieties. In 2018 Yiqiang Li c…
Intersection cohomology groups of instanton moduli spaces and cotangent bundles of affine flag varieties
Hiraku Nakajima
This is an abstract for my talk at the 68th Geometry Symposium on August 31, 2021. It is based on my joint work in progress with Dinakar Muthiah: a conjectural characterization of…
A mathematical definition of Coulomb branches of supersymmetric gauge theories and geometric Satake correspondences for Kac-Moody Lie algebras
Hiraku Nakajima
This is an introductory article for a mathematical definition of Coulomb branches of 3d N=4 SUSY gauge theories and geometric Satake correspondences for Kac-Moody Lie algebras base…
Kazhdan-Lusztig conjecture via Zastava spaces
Alexander Braverman, Michael Finkelberg, Hiraku Nakajima
We deduce the Kazhdan-Lusztig conjecture on the multiplicities of simple modules over a simple complex Lie algebra in Verma modules in category O from the equivariant geometric Sat…
Towards geometric Satake correspondence for Kac-Moody algebras -- Cherkis bow varieties and affine Lie algebras of type
Hiraku Nakajima
We give a provisional construction of the Kac-Moody Lie algebra module structure on the hyperbolic restriction of the intersection cohomology complex of the Coulomb branch of a fra…
Line bundles over Coulomb branches
Alexander Braverman, Michael Finkelberg, Hiraku Nakajima
This is the third companion paper of arXiv:1601.03586. When a gauge theory has a flavor symmetry group, we construct a partial resolution of the Coulomb branch as a variant of the…