Papers โบ An investigation into Lie algebra representations obtained from regular holonomic D-modules
An investigation into Lie algebra representations obtained from regular holonomic D-modules
Julian Wykowski, Travis Schedler
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Beilinson--Bernstein localisation relates representations of a Lie algebra ๐ค to certain ๐-modules on the flag variety of ๐ค. In [arXiv:2002.01540], examples of ๐ฐ๐ฉโ-representations which correspond to ๐-modules on โโยน 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 ๐ฐ๐ฉโ-representations which correspond to holonomic ๐-modules on โโยน 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.
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