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


Authors: Michael Dettweiler and Stefan Reiter
Journal: Trans. Amer. Math. Soc. 366 (2014), 5821-5851
MSC (2010): Primary 32S40, 20G41
Published electronically: July 29, 2014
MathSciNet review: 3256185
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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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Additional Information

Michael Dettweiler
Affiliation: Department of Mathematics, University of Bayreuth, 95440 Bayreuth, Germany
Email: michael.dettweiler@uni-bayreuth.de

Stefan Reiter
Affiliation: Department of Mathematics, University of Bayreuth, 95440 Bayreuth, Germany
Email: stefan.reiter@uni-bayreuth.de

DOI: https://doi.org/10.1090/S0002-9947-2014-06042-X
Keywords: Ordinary differential equation, exceptional algebraic group, local system, middle convolution
Received by editor(s): September 27, 2012
Received by editor(s) in revised form: November 13, 2012, and November 27, 2012
Published electronically: July 29, 2014
Article copyright: © Copyright 2014 American Mathematical Society