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.
Note on Twisted Elliptic Genus of K3 Surface
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abstract
We discuss the possibility of Mathieu group M24 acting as symmetry group on the K3 elliptic genus as proposed recently by Ooguri, Tachikawa and one of the present authors. One way of testing this proposal is to derive the twisted elliptic genera for all conjugacy classes of M24 so that we can determine the unique decomposition of expansion coefficients of K3 elliptic genus into irreducible representations of M24. In this paper we obtain all the hitherto unknown twisted elliptic genera and find a strong evidence of Mathieu moonshine.
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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.