Work

The affine Springer fiber – sheaf correspondence

Year: 2025

Type: article

Abstract: Given a semisimple element in the loop Lie algebra of a reductive group, we construct a quasi-coherent sheaf on a partial resolution of the trigonometric commuting variety of the Langlands dual group. The construction uses affine Springer theory and can be thought of as an incarnation of 3d mirror symmetry. For the group $GL_n$, the corresponding partial resolution is $\mathrm{Hilb}^n(\mathbb{C}^\times\times \mathbb{C})$. We also consider a quantization of this construction for homogeneous elements.

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2025.110143

Authors: Eugene Gorsky, Oscar Kivinen, Alexei Oblomkov

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funders: National Science Foundation, Suomalainen Tiedeakatemia

Awards: FRG: Collaborative Research: Algebra and Geometry Behind Link Homology, Structures in Khovanov-Rozansky homology, CAREER: Knot invariants, moduli spaces of sheaves and representation theory, FRG: Collaborative Research: Algebra and Geometry Behind Link Homology