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arXiv · 2604.11966

Affine Springer fiber and the small quantum group

Roman Bezrukavnikov·Pablo Boixeda Alvarez·Michael McBreen·Zhiwei Yun
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Abstract

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.

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Roman Bezrukavnikov, Pablo Boixeda Alvarez, Michael McBreen, Zhiwei Yun. 2026-04-13. Affine Springer fiber and the small quantum group. https://arxiv.org/abs/2604.11966

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