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arXiv · 2404.09582

Stokes phenomenon of Kloosterman and Airy connections

Andreas Hohl·Konstantin Jakob
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Abstract

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

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Andreas Hohl, Konstantin Jakob. 2024-04-15. Stokes phenomenon of Kloosterman and Airy connections. https://arxiv.org/abs/2404.09582

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