Examples of hypergeometric twistor $\mathcal{D}$-modules

TL;DR

This paper demonstrates that specific hypergeometric differential systems are linked to irregular mixed Hodge modules and computes their Hodge filtration, also comparing two Fourier-Laplace transformation types for algebraic integrable twistor D-modules.

Contribution

It establishes the connection between hypergeometric systems and irregular mixed Hodge modules and provides a comparison theorem for Fourier-Laplace transformations.

Findings

Hypergeometric systems underlie irregular mixed Hodge modules.

Irregular Hodge filtration for these systems is computed.

A comparison theorem for Fourier-Laplace transformations is provided.

Abstract

We show that certain one-dimensional hypergeometric differential systems underlie objects of the category of irregular mixed Hodge modules, which was recently introduced by Sabbah, and compute the irregular Hodge filtration for them. We also provide a comparison theorem between two different types of Fourier-Laplace transformation for algebraic integrable twistor $\mathcal{D}$-modules.