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

Alexei Oblomkov; Lev Rozansky

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arXiv · 2510.13039

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

Alexei Oblomkov·Lev Rozansky

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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 $Gr(k,N)$.

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BibTeX RIS

Alexei Oblomkov, Lev Rozansky. 2025-10-14. A categorification of representations of $U_q(\mathfrak{gl}_{1|1})$. https://arxiv.org/abs/2510.13039

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