• [AK]: Vector Bundle on $\P^2$
• [EG]: Affine Springer Fiber
• [WL]: Ruling and Stratification

It is always a good idea to share your thoughts, it might induce more sparks.

Consider the moduli space of rank $n$ vector bundles on $\P^2$. It is given by a disjoint union of components, labelled by $(\lambda, \mu, \nu) \in (X^*(T)/W)^3$, dominant weights $$ (L_\lambda \times L_\mu \times L_\nu) / GL(n) $$ where $L_\chi$ is the equivariant line bundle over the flag variety $GL_n/B$.