Parabolic bundles on $\mathbb P^2$, Quiver varieties, and quantization

The moduli space of certain parabolic torsion free sheaves on $\mathbb P^2$ plays an important role in the geometric representation theory (under the name of Affine Laumon space). The singularities of its affinization contain the “limit singularities” of Schubert varieties of the affine Grassmannian of $\mathrm{SL}_n$. It can be realized as a quiver variety, and quantized via the quantum Hamiltonian reduction. The quantization is described in terms of affine Yangians.