• Corpus ID: 244714753

An investigation into Lie algebra representations obtained from regular holonomic D-modules

@inproceedings{Wykowski2021AnII,
  title={An investigation into Lie algebra representations obtained from regular holonomic D-modules},
  author={Julian Wykowski and Travis Schedler},
  year={2021}
}

• J. Wykowski, T. Schedler
• Published 30 November 2021
• Mathematics

Beilinson–Bernstein localisation [BB81] relates representations of a Lie algebra g to certain D-modules on the flag variety of g. In [Rom21], examples of sl2-representations which correspond to D-modules on CP 1 were computed. In this expository article, we give a topological description of these and extended examples via the Riemann–Hilbert correspondence. We generalise this to a full characterisation of sl2-representations which correspond to holonomic D-modules on CP with at most 2 regular singularities. We construct further examples with more singularities and develop a computer program for the computation of this correspondence in more general cases.