Jordan-Hölder property for shifted quantum affine algebras
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916588633980928 |
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| author | Hernandez, David Zhang, Huafeng |
| author_facet | Hernandez, David Zhang, Huafeng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16859 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Jordan-Hölder property for shifted quantum affine algebras Hernandez, David Zhang, Huafeng Quantum Algebra Mathematical Physics Representation Theory 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. |
| title | Jordan-Hölder property for shifted quantum affine algebras |
| topic | Quantum Algebra Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2501.16859 |