Rigidity index preservation of regular holonomic D-modules

TL;DR

This paper proves algebraically that the Fourier transform maintains the rigidity index of certain regular holonomic D-modules on the projective line, highlighting a key invariance property.

Contribution

It establishes the algebraic preservation of the rigidity index under Fourier transform for irreducible regular holonomic D-modules on the projective line.

Findings

Fourier transform preserves rigidity index of these modules

Rigidity index is an invariant under Fourier transform in this context

Provides algebraic proof of this invariance

Abstract

This paper shows algebraically that the Fourier transform preserves the rigidity index of irreducible regular holonomic $\mathcal{D}_{\mathbb{P}^1}[*\{\infty\}]$-modules.