2021/11/29 by Wykowski, Julian, Schedler, Travis
#14F10 (Primary) 17B10 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2111.14774
Beilinson--Bernstein localisation relates representations of a Lie algebra \mathfrakg to certain D-modules on the flag variety of \mathfrakg. In [arXiv:2002.01540], examples of \mathfraksl2-representations which correspond to D-modules on \mathbbCP1 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 \mathfraksl2-representations which correspond to holonomic D-modules on \mathbbCP1 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.