237 citations · 1.2k across the 58 of their papers we have counts for
14 papers · 1 filter
Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum affine algebras
Hiraku Nakajima
We prove the conjecture by Gyenge, Némethi and Szendrői in arXiv:1512.06844, arXiv:1512.06848 giving a formula of the generating function of Euler numbers of Hilbert schemes of poi…
Geometric Satake correspondence for affine Kac-Moody Lie algebras of type
Hiraku Nakajima
This is an informal expository article on geometric Satake correspondence for affine Kac-Moody Lie algebras of type given in arXiv:1810.04293. We emphasize formal analogies bet…
A simple proof of the formula for the Betti numbers of the quasihomogeneous Hilbert schemes
A. Buryak, B. L. Feigin, H. Nakajima
In a recent paper the first two authors proved that the generating series of the Poincare polynomials of the quasihomogeneous Hilbert schemes of points in the plane has a simple de…
Refined Chern-Simons theory and Hilbert schemes of points on the plane
Hiraku Nakajima
Aganagic and Shakirov propose a refinement of the SU(N) Chern-Simons theory for links in three manifolds with S^1-symmetry, such as torus knots in S^3, based on deformation of the…
Perverse coherent sheaves on blow-up. III. Blow-up formula from wall-crossing
Hiraku Nakajima, Kota Yoshioka
In earlier papers arXiv:0802.3120, arXiv:0806.0463 of this series we constructed a sequence of intermediate moduli spaces $\bM^m(c)$ connecting a moduli space of stable tors…
Counting invariant of perverse coherent sheaves and its wall-crossing
Kentaro Nagao, Hiraku Nakajima
We introduce moduli spaces of stable perverse coherent systems on small crepant resolutions of Calabi-Yau 3-folds and consider their Donaldson-Thomas type counting invariants. The…