Global bases for Bosonic extensions of quantum unipotent coordinate rings
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911925204418560 |
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| author | Kashiwara, Masaki Kim, Myungho Oh, Se-jin Park, Euiyong |
| author_facet | Kashiwara, Masaki Kim, Myungho Oh, Se-jin Park, Euiyong |
| contents | In the paper, we establish the global basis theory for the bosonic extension $\widehat{\mathcal{A}}$ associated with an arbitrary generalized Cartan matrix. When $\widehat{\mathcal{A}}$ is of simply-laced finite type, it is isomorphic to the quantum Grothendieck ring of the Hernandez-Leclerc category over a quantum affine algebra. In this case, we show that the $(t,q)$-characters of simple modules in the Hernandez-Leclerc category correspond to the normalized global basis of $\widehat{\mathcal{A}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13160 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global bases for Bosonic extensions of quantum unipotent coordinate rings Kashiwara, Masaki Kim, Myungho Oh, Se-jin Park, Euiyong Representation Theory 05E10, 05E18, 17B37} In the paper, we establish the global basis theory for the bosonic extension $\widehat{\mathcal{A}}$ associated with an arbitrary generalized Cartan matrix. When $\widehat{\mathcal{A}}$ is of simply-laced finite type, it is isomorphic to the quantum Grothendieck ring of the Hernandez-Leclerc category over a quantum affine algebra. In this case, we show that the $(t,q)$-characters of simple modules in the Hernandez-Leclerc category correspond to the normalized global basis of $\widehat{\mathcal{A}}$. |
| title | Global bases for Bosonic extensions of quantum unipotent coordinate rings |
| topic | Representation Theory 05E10, 05E18, 17B37} |
| url | https://arxiv.org/abs/2406.13160 |