# Sporadic and Exceptional

## In dedication to the memory of my dear friend Professor John S. McKay

## DOI:

https://doi.org/10.56725/instemm.v1iS1.8## Keywords:

Generalised Moonshine, Lie algebra, Monster, Baby, Fischer group, del Pezzo surfaces, McKay-Thompson series, Conway's sporadic group, Horrocks-Mumford bundle## Abstract

We study the web of correspondences linking the exceptional Lie algebras E_{8,7,6} 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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