Some fourth order CY-type operators with non symplectically rigid monodromy

TL;DR

This paper investigates specific matrix tuples with rigidity properties in symplectic groups, exploring their connection to Calabi-Yau differential operators through algebraic and convolutional constructions, leading to new examples.

Contribution

It introduces new examples of CY-type differential operators with non-symplectically rigid monodromy using algebraic and middle convolution techniques.

Findings

Construction of new CY-type operators with specific monodromy properties

Identification of tuples with rigidity index two in Sp_4(C)

Extension of known examples through algebraic operations and convolutions

Abstract

We study tuples of matrices with rigidity index two in $\Sp_4(\mathbb{C})$, 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 differential operators lead to previously known and new examples.