English

Stokes phenomenon of Kloosterman and Airy connections

Algebraic Geometry 2026-02-03 v2

Abstract

We define categories of Stokes filtered and Stokes graded GG-local systems for reductive groups GG and use the formalism of Tannakian categories to show that they are equivalent to the category of GG-connections. We then use the interpretation of moduli spaces of Stokes filtered GG-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