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arXiv · 2501.16859

Jordan-H\"older property for shifted quantum affine algebras

David Hernandez·Huafeng Zhang
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Abstract

We prove that finite length representations of shifted quantum affine algebras in category $\mathcal{O}^{\mathrm{sh}}$ are stable by fusion product. This implies that in the topological Grothendieck ring $K_0(\mathcal{O}^{\mathrm{sh}})$ the Grothendieck group of finite length representations forms a non-topological subring. We also conjecture this subring is isomorphic to the cluster algebra discovered in arXiv:2401.04616. In the course of our proofs, we establish that any simple representation in category $\mathcal{O}^{\mathrm{sh}}$ descends to a truncation, for certain truncation parameters as conjectured in arXiv:2010.06996 in terms of Langlands dual $q$-characters.

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David Hernandez, Huafeng Zhang. 2025-01-28. Jordan-H\"older property for shifted quantum affine algebras. https://arxiv.org/abs/2501.16859

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