Sporadic and Exceptional
In dedication to the memory of my dear friend Professor John S. McKay
DOI:
https://doi.org/10.56725/instemm.v1iS1.8Keywords:
Generalised Moonshine, Lie algebra, Monster, Baby, Fischer group, del Pezzo surfaces, McKay-Thompson series, Conway's sporadic group, Horrocks-Mumford bundleAbstract
We study the web of correspondences linking the exceptional Lie algebras E8,7,6 and the sporadic simple groups Monster, Baby and the largest Fischer group. This is done via the investigation of classical enumerative problems on del Pezzo surfaces in relation to the cusps of certain subgroups of PSL(2,R) for the relevant McKay-Thompson series in Generalized Moonshine. We also study Conway's sporadic group, as well as its association with the Horrocks-Mumford bundle.
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