Stokes phenomenon of Kloosterman and Airy connections
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...
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Sprache: | eng |
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Zusammenfassung: | 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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DOI: | 10.48550/arxiv.2404.09582 |