  Khovanov-Lauda define a 2-category $\mathcal{U}$ such that the split
Grothendieck group $K_0(\mathcal{U})$ is isomorphic to an integral version of
the quantized universal enveloping algebra $\mathbf{U}(\mathfrak{sl}_n)$, $n
\geq 2$. Beliakova-Habiro-Lauda-Webster prove that the trace decategorification
of the Khovanov-Lauda 2-category is isomorphic to the the current algebra
$\mathbf{U}(\mathfrak{sl}_n [t])$ - the universal enveloping algebra of the Lie
algebra $ \mathfrak{sl}_n \otimes \mathbb{C} [t]$. A 2-representation of
$\,\mathcal{U}$ is a 2-functor from $\mathcal{U}$ to a linear, additive
2-category. In this note we are interested in the 2-representation, defined by
Khovanov-Lauda using bimodules over cohomology rings of flag varieties. This
2-representation induces an action of the current algebra
$\mathbf{U}(\mathfrak{sl}_n [t])$ on the cohomology rings. We explicitly
compute the action of $\mathbf{U}(\mathfrak{sl}_n [t])$ generators using the
trace functor. It turns out that the obtained current algebra module is related
to another family of $\mathbf{U}(\mathfrak{sl}_n [t])$-modules, called local
Weyl modules. Using known results about the cohomology rings, we are able to
provide a new proof of the character formula for the local Weyl modules.
