Affine Springer fiber and the small quantum group

Fuente: arXiv
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Autori principali: Bezrukavnikov, Roman, Alvarez, Pablo Boixeda, McBreen, Michael, Yun, Zhiwei
Natura: Preprint
Pubblicazione: 2026
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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