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 satisfies a Riemann-Hilbert correspondence for holonomy Lie algebras.
Stable hyperplane arrangements.arXiv preprint, 2510.11099
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Middle convolution for Lie algebra representations
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 satisfies a Riemann-Hilbert correspondence for holonomy Lie algebras.