The classification of orthogonally rigid 𝐺₂-local systems and related differential operators

Dettweiler, Michael; Reiter, Stefan

doi:10.1090/S0002-9947-2014-06042-X

The classification of orthogonally rigid $G_2$-local systems and related differential operators
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Trans. Amer. Math. Soc. 366 (2014), 5821-5851 Request permission

Abstract:

We prove a criterion for a general self-adjoint differential operator of rank $7$ to have its monodromy group inside the exceptional algebraic group $G_2(\mathbb {C}).$ We then classify orthogonally rigid local systems of rank $7$ on the punctured projective line whose monodromy is dense in the exceptional algebraic group $G_2(\mathbb {C}).$ We obtain differential operators corresponding to these local systems under Riemann-Hilbert correspondence.

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