A categorification of representations of $U_q(\mathfrak{gl}_{1|1})$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912648210153472 |
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| author | Oblomkov, Alexei Rozansky, Lev |
| author_facet | Oblomkov, Alexei Rozansky, Lev |
| contents | 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 $Gr(k,N)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A categorification of representations of $U_q(\mathfrak{gl}_{1|1})$ Oblomkov, Alexei Rozansky, Lev Representation Theory Algebraic Geometry Category Theory General Topology 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 $Gr(k,N)$. |
| title | A categorification of representations of $U_q(\mathfrak{gl}_{1|1})$ |
| topic | Representation Theory Algebraic Geometry Category Theory General Topology |
| url | https://arxiv.org/abs/2510.13039 |