Mathematical Research Letters

Volume 19 (2012)

Number 1

Modular invariant $D$-modules

Pages: 9 – 12



Takashi Ichikawa (Department of Mathematics, Graduate School of Science and Engineering, Saga University, Saga 840-8502, Japan)


We study $D$-modules over the modular curve of level $1$defined as an orbifold, and show that if such $D$-modulesare of rank $1$, these monodromy representations map the$S$-action to the identity. This means that in the orbifoldcase, there are linear representations of the fundamentalgroups which do not come from $D$-modules.

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