Real Slices of SL(๐‘Ÿ, โ„‚)-Opers

Through the action of an anti-holomorphic involution ๐œŽ (a real structure) on a Riemann surface ๐›ธ, we consider the induced actions on SL(๐‘Ÿ, โ„‚)-opers and study the real slices fixed by such actions. By constructing this involution for different descriptions of the space of SL(๐‘Ÿ, โ„‚)-opers, we can give...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2023
Main Authors: Biswas, Indranil, Heller, Sebastian, Schaposnik, Laura P.
Format: Article
Language:English
Published: ะ†ะฝัั‚ะธั‚ัƒั‚ ะผะฐั‚ะตะผะฐั‚ะธะบะธ ะะะ ะฃะบั€ะฐั—ะฝะธ 2023
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/212017
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Real Slices of SL(๐‘Ÿ, โ„‚)-Opers. Indranil Biswas, Sebastian Heller and Laura P. Schaposnik. SIGMA 19 (2023), 067, 23 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:Through the action of an anti-holomorphic involution ๐œŽ (a real structure) on a Riemann surface ๐›ธ, we consider the induced actions on SL(๐‘Ÿ, โ„‚)-opers and study the real slices fixed by such actions. By constructing this involution for different descriptions of the space of SL(๐‘Ÿ, โ„‚)-opers, we can give a natural parametrization of the fixed point locus via differentials on the Riemann surface, which in turn allows us to study their geometric properties.
ISSN:1815-0659