Any twisted Dijkgraaf-Witten representation of a mapping class group of an orientable, compact surface with boundary has finite image.
Bantay also calculated the images of certain representations of mapping class groups on the Hilbert space of an orbifold model associated to @math @cite_10 . These representations appear to coincide with the twisted Dijkgraaf-Witten representations. However, due to lack of proof, the precise connection is unclear.
@cite_10
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Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite-dimensional extension of the quantum group is presented.