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arxiv: 2601.00544 · v3 · pith:MCMRCWREnew · submitted 2026-01-02 · 🧮 math.AG · math.CA

On the Riemann-Hilbert problem for hyperplane arrangements with a good line

Shunya Adachi , Kazuki Hiroe This is my paper
classification 🧮 math.AG math.CA
keywords problemhyperplanearrangementscomplementslocalriemann-hilbertsystemasks
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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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  1. Middle convolution for Lie algebra representations

    math.RT 2026-05 unverdicted novelty 7.0

    The paper introduces a Lie algebra analogue of the middle convolution functor and proves it generalizes the Long-Moody functor, recovers Dettweiler-Reiter convolution, is compatible with Haraoka's version, and satisfi...