This paper introduces a Lie algebra analogue of the middle convolution functor on modules over free, Drinfeld-Kohno, and holonomy Lie algebras, shows it generalizes prior constructions, and establishes a Riemann-Hilbert correspondence for holonomy Lie algebras.
On the riemann-hilbert problem for hyperplane arrangements with a good line.arXiv preprint, 2601.00544
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abstract
We study a variant of the Riemann-Hilbert problem on the complements of hyperplane arrangements. This problem asks whether a given local system on the complement can be realized as the solution sheaf of a logarithmic Pfaffian system with constant coefficients. In this paper, we generalize Katz's middle convolution as a functor for local systems on hyperplane complements and show that it preserves the solvability of this problem.
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Middle convolution for Lie algebra representations
This paper introduces a Lie algebra analogue of the middle convolution functor on modules over free, Drinfeld-Kohno, and holonomy Lie algebras, shows it generalizes prior constructions, and establishes a Riemann-Hilbert correspondence for holonomy Lie algebras.