Betti Structures of Hypergeometric Equations

Abstract

Abstract We study Betti structures in the solution complexes of confluent hypergeometric equations. We use the framework of enhanced ind-sheaves and the irregular Riemann–Hilbert correspondence of D’Agnolo–Kashiwara. The main result is a group theoretic criterion that ensures that enhanced solutions of such systems are defined over certain subfields of $\mathds{ C}$. The proof uses a description of the hypergeometric systems as exponentially twisted Gauß–Manin systems of certain Laurent polynomials.