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The classification of orthogonally rigid $G_2$-local systems and related differential operators

2014
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Transactions of the American Mathematical Society
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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 (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 (C). can be seen as rigidity relative to the larger group GL n ) but still strong enough to impose a lot of structure on L. By the work of N. Katz on the middle convolution functor MC χ

doi:10.1090/s0002-9947-2014-06042-x
fatcat:nrebeph3kvctniwhgxwpqgp6ri