Affine Springer fiber and the small quantum group
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866910126197178368 |
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| author | Bezrukavnikov, Roman Alvarez, Pablo Boixeda McBreen, Michael Yun, Zhiwei |
| author_facet | Bezrukavnikov, Roman Alvarez, Pablo Boixeda McBreen, Michael Yun, Zhiwei |
| contents | We find a new geometric incarnation for the principal block in the category of modules over a quantum group at a root of unity, realizing it as a full subcategory of microsheaves on a certain affine Springer fiber. We also prove a related geometric Langlands type equivalence with wild ramification, identifying the latter category with a category of coherent sheaves on the Springer resolution for the dual group. This can also be viewed as a version of homological mirror symmetry for the Springer resolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11966 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Affine Springer fiber and the small quantum group Bezrukavnikov, Roman Alvarez, Pablo Boixeda McBreen, Michael Yun, Zhiwei Algebraic Geometry Representation Theory We find a new geometric incarnation for the principal block in the category of modules over a quantum group at a root of unity, realizing it as a full subcategory of microsheaves on a certain affine Springer fiber. We also prove a related geometric Langlands type equivalence with wild ramification, identifying the latter category with a category of coherent sheaves on the Springer resolution for the dual group. This can also be viewed as a version of homological mirror symmetry for the Springer resolution. |
| title | Affine Springer fiber and the small quantum group |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2604.11966 |