Stokes phenomenon of Kloosterman and Airy connections
Algebraic Geometry
2026-02-03 v2
Abstract
We define categories of Stokes filtered and Stokes graded -local systems for reductive groups and use the formalism of Tannakian categories to show that they are equivalent to the category of -connections. We then use the interpretation of moduli spaces of Stokes filtered -local systems as braid varieties to prove physical rigidity of two well-known families of cohomologically rigid connections, the Kloosterman and Airy connections. In the Kloosterman case, our proof relies on Steinberg's cross-section.
Keywords
Cite
@article{arxiv.2404.09582,
title = {Stokes phenomenon of Kloosterman and Airy connections},
author = {Andreas Hohl and Konstantin Jakob},
journal= {arXiv preprint arXiv:2404.09582},
year = {2026}
}
Comments
29 pages; v2: corrected the setup for Stokes filtrations (Section 3.3), substantially extended the results of Section 5