A categorification of representations of $U_q({\mathfrak{gl}}_{1|1})$

Abstract

We categorify the action of $U_q({\mathfrak{gl}}_{1|1})$ on the tensor product of its vector representations $({\mathbb{C}}^{1|1}{)}^{\otimes N}$. 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 $Gr(k,N)$.

12 pages, no figures; comments are welcome!