Opers as a generalisation of complex projective structures
Essentially, complex projective structures arise as geometries modeled in the projective line. Meanwhile, opers appear as local systems of representation-theoretic nature and are linked to principal bundles with connections. These objects where first introduced in the punctured disk by Drinfeld and...
- Autores:
-
Aragón Rodríguez, Manuel Alejandro
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2024
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/73825
- Acceso en línea:
- https://hdl.handle.net/1992/73825
- Palabra clave:
- Opers
Principal bundles
Complex geometry
Lie groups
Riemann surfaces
Matemáticas
- Rights
- openAccess
- License
- Attribution-NonCommercial-NoDerivatives 4.0 International
| Summary: | Essentially, complex projective structures arise as geometries modeled in the projective line. Meanwhile, opers appear as local systems of representation-theoretic nature and are linked to principal bundles with connections. These objects where first introduced in the punctured disk by Drinfeld and Sokolov in their study of KdV-type hierarchies and were later given a coordinate-free description for a general reductive group by Beilinson and Drinfeld. Recently, they have been studied in their connection to the geometrical Langlands correspondence and their role in the theory of vertex algebras, as developed by Frenkel. In this thesis, we study the connection between complex projective structures and opers in a geometric and algebraic way and explain how opers generalise complex projective structures when a general complex Lie group is studied. |
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