The M24 and M23 lattice symmetries of the odd Leech lattice do not lift to automorphisms of its lattice vertex operator algebra; the relevant group extensions are non-split.
Mathieu twining characters for K3
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abstract
The analogue of the McKay-Thompson series for the proposed Mathieu group action on the elliptic genus of K3 is analysed. The corresponding NS-sector twining characters have good modular properties and satisfy remarkable replication identities. These observations provide strong support for the conjecture that the elliptic genus of K3 carries indeed an action of the Mathieu group M24.
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On the Symmetry of Odd Leech Lattice CFT
The M24 and M23 lattice symmetries of the odd Leech lattice do not lift to automorphisms of its lattice vertex operator algebra; the relevant group extensions are non-split.