THE MOONSHINE MODULE FOR CONWAY’S GROUP

We exhibit an action of Conway’s group – the automorphism group of the Leech lattice – on a distinguished super vertex operator algebra, and we prove that the associated graded trace functions are normalized principal moduli, all having vanishing constant terms in their Fourier expansion. Thus we co...

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Bibliographic Details
Published inForum of mathematics. Sigma Vol. 3
Main Authors DUNCAN, JOHN F. R., MACK-CRANE, SANDER
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.06.2015
Subjects
11F11
11F22
17B69
20C34
Algebra
20C34
17B69
11F11
11F22
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Summary:We exhibit an action of Conway’s group – the automorphism group of the Leech lattice – on a distinguished super vertex operator algebra, and we prove that the associated graded trace functions are normalized principal moduli, all having vanishing constant terms in their Fourier expansion. Thus we construct the natural analogue of the Frenkel–Lepowsky–Meurman moonshine module for Conway’s group. The super vertex operator algebra we consider admits a natural characterization, in direct analogy with that conjectured to hold for the moonshine module vertex operator algebra. It also admits a unique canonically twisted module, and the action of the Conway group naturally extends. We prove a special case of generalized moonshine for the Conway group, by showing that the graded trace functions arising from its action on the canonically twisted module are constant in the case of Leech lattice automorphisms with fixed points, and are principal moduli for genus-zero groups otherwise.
ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2015.7