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Generalised Mathieu Moonshine

The Mathieu twisted twining genera, i.e. the analogues of Norton's generalised Moonshine functions, are constructed for the elliptic genus of K3. It is shown that they satisfy the expected consistency conditions, and that their behaviour under modular transformations is controlled by a 3-cocycle in H^3(M_24,U(1)), just as for the case of holomorphic orbifolds. This suggests that a holomorphic VOA may be underlying Mathieu Moonshine.