Some Fourth Order CY-type Operators with Non-symplectically Rigid Monodromy

ABSTRACT

We study tuples of matrices with rigidity index two in , which are potentially induced by differential operators of Calabi–Yau type. The constructions of those monodromy tuples via algebraic operations and middle convolutions and the related constructions on the level of differential operators lead to previously known and new examples.

KEYWORDS:

• Calabi–Yau operators
• local systems
• rigidity
• middle convolution
• Hadamard product

2000 AMS Subject Classification:

• 32S40
• 34M35
• 34M15
• 14J32

Acknowledgments

We thank Duco van Straten for constant interest, support, and suggestions concerning the content of this article. We are also indebted to Gert Almkvist for many inspiring conversations and attempts concerning the art of finding CY-type equations as well as his great effort to identify them.