A categorification of representations of U_q(\mathfrakgl_1|1)

2025/10/14 by Alexei Oblomkov, Oblomkov, Alexei, Lev Rozansky +1
Mathematics · #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2510.13039

Abstract

We categorify the action of U_q(\mathfrakgl_1|1) on the tensor product of its vector representations (ℂ^1|1)^{⊗ 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).

Citations

• Higher representations and cornered Heegaard Floer homology
• A categorification of the positive half of quantum gl(m|1)

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