The classification of orthogonally rigid $G_2$-local systems and related differential operators
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- by Michael Dettweiler and Stefan Reiter PDF
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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.References
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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
- 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
- © Copyright 2014 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 366 (2014), 5821-5851
- MSC (2010): Primary 32S40, 20G41
- DOI: https://doi.org/10.1090/S0002-9947-2014-06042-X
- MathSciNet review: 3256185