A categorification of representations of $U_q({\mathfrak{g}\mathfrak{l}}_{1\mathrm{\mid }1})$

We categorify the action of $U_q({\mathfrak{g}\mathfrak{l}}_{1\mathrm{\mid }1})$ on the tensor product of its vector representations $({\mathbb{C}}^{1\mathrm{\mid }1}{)}^{\otimes N}$. The generators $E$ and $F$ are represented by Fourier-Mukai functors between the derived categories of coherent sheaves on the total spaces of “semi-parabolic” vector bundles over the Grassmannians $Gr(k,N)$.