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arXiv · 2402.03668

BGG Reciprocity for Generalized Weight Modules of Unrolled Restricted Quantum Groups at Roots of Unity

Matthew Rupert
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Abstract

We consider the category of generalized weight modules over the unrolled restricted quantum group $\overline{U}_q^H(\mathfrak{g})$ of a finite-dimensional simple complex Lie algebra $\mathfrak{g}$ at root of unity q. Although this category does not admit projective modules, it is filtered by subcategories with enough projectives. We show that the projective modules in these subcategories satisfy a variant of BGG reciprocity and give a generators and relations description of the projective covers of irreducible modules when $\mathfrak{g}=\mathfrak{sl}_2$.

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Matthew Rupert. 2024-02-06. BGG Reciprocity for Generalized Weight Modules of Unrolled Restricted Quantum Groups at Roots of Unity. https://arxiv.org/abs/2402.03668

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