In Nakajima's Geometric construction of algebras(pages 3-7), he uses the subalgebra of the convolution algebra of $Gr(k^N)\times Gr(k^N)$ invariant under $GL_N$ action to construct $U_q(sl_2)$. To do this, he finds imposes relations to form some special operators, which he shows are isomorphic to the generators of $U_q(sl_2)$. In particular, he uses characteristic functions on certain subsets of $k^N$ with dimensionality conditions. These conditions smell like Schubert conditions.

Can we see these as the Schubert conditions in some way?

I have compared them, but I don't see the link.

EDIT: Read the comments below for a related paper.

`$\mathfrak{sl}_2$`

to be helpful. – Jim Humphreys Oct 29 '10 at 13:51