Affine Springer fiber and the small quantum group
Algebraic Geometry
2026-04-15 v1 Representation Theory
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.
Cite
@article{arxiv.2604.11966,
title = {Affine Springer fiber and the small quantum group},
author = {Roman Bezrukavnikov and Pablo Boixeda Alvarez and Michael McBreen and Zhiwei Yun},
journal= {arXiv preprint arXiv:2604.11966},
year = {2026}
}