# Perverse sheaves on instanton moduli spaces and AGT conjecture

Abstract: We consider Uhlenbeck partial compactifications of framed
moduli spaces of instantons on $\mathbb R^4$ with a type $ADE$ gauge
group. We show that a natural class of perverse sheaves behaves nicely
under the hyperbolic restriction functor with respect to a Levi
subgroup. As an application, we obtain a representation of a W-algebra
on the direct sum of intersection cohomology groups, combined with earlier
works by Maulik-Okounkov, Schiffmann-Vasserot for type $A$. This proves
the AGT conjecture for type $ADE$. Work in progress with Braverman,
Finkelberg.

nakajima@math.kyoto-u.ac.jp