Abstract
Given a discrete subgroup Γ of finite co-volume of PGL(2,R), we define and study parabolic vector bundles on the quotient Σ of the (extended) hyperbolic plane by Γ. If Γ contains an orientation-reversing isometry, then the above is equivalent to studying real and quaternionic parabolic vector bundles on the orientation cover of degree two of Σ. We then prove that isomorphism classes of polystable real and quaternionic parabolic vector bundles are in a natural bijective correspondence with the equivalence classes of real and quaternionic unitary representations of Γ. Similar results are obtained for compact-type real parabolic vector bundles over Klein surfaces.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
