Parabolic vector bundles on Klein surfaces
| Autor: | Biswas, Indranil, Schaffhauser, Florent |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Illinois J. Math. 64, no. 1 (2020), 105-118 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1215/00192082-8165614 |
| Popis: | Given a discrete subgroup $\Gamma$ of finite co-volume of $\mathrm{PGL}(2,\mathbb{R})$, we define and study parabolic vector bundles on the quotient $\Sigma$ of the (extended) hyperbolic plane by $\Gamma$. If $\Gamma$ contains an orientation-reversing isometry, then the above is equivalent to studying real and quaternionic parabolic vector bundles on the orientation cover of $\Sigma$. We then prove that isomorphism classes of polystable real and quaternionic parabolic vector bundles are in bijective correspondence with equivalence classes of real and quaternionic unitary representations of $\Gamma$. Similar results are obtained for compact-type real parabolic vector bundles over Klein surfaces. Comment: Final version; to appear in Illinois Journal of Mathematics |
| Databáze: | arXiv |
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