#### Vol. 13, No. 6, 2019

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

### Alberto Castaño Domínguez, Thomas Reichelt and Christian Sevenheck

Vol. 13 (2019), No. 6, 1415–1442
DOI: 10.2140/ant.2019.13.1415
##### 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 $\mathsc{D}$-modules.

##### Keywords
D-modules, irregular Hodge filtration, twistor D-modules, Fourier–Laplace transformation, hypergeometric D-modules
Primary: 14F10
Secondary: 32C38