Tautological systems and free divisors

Abstract

We introduce tautological system defined by prehomogenous actions of reductive algebraic groups. If the complement of the open orbit is a linear free divisor satisfying a certain finiteness condition, we show that these systems underly mixed Hodge modules. A dimensional reduction is considered and gives rise to one-dimensional differential systems generalizing the quantum differential equation of projective spaces.

References in corpus (2)

• Hypergeometric D-modules and twisted Gauss-Manin systems
• Irregular Hodge filtration of some confluent hypergeometric systems