• Action by correspondence, history of quiver Hecke algebra
• Lie superalgebra

Let $\Gamma$ be the quiver with a single dot. The $A_1$ quiver. Corresponding to the single root of $sl_2$.

We consider the moduli stack of quiver representation, it is classified by the dimension vector, and in this case it is just $d \in \Z_{\geq 0}$. Let $X_d = [pt / GL(d)]$. Map from a space $X$ to this stack (ok, I like it better than BGL(d)) is the same as having a principal $GL(d)$ bundle on $X$, or we can get an associated $\C^d$-bundle, from which we can always recover the $GL(d)$ bundle as the endomorphism bundle.

What is the constructible sheaf on the stack $X_d$? What is the stratification? Is it just local system?

Now, suppose we have $X_{d_1}, X_{d_2}$ and $X_{d}$ where $d=d_1 + d_2$. What's the relation between the three moduli spaces? Well, consider the parabolic subgroup $P \In GL(d)$, of block size $d_1, d_2$