Sporadic and Exceptional

2015/05/25 by Yang-Hui He, Yang‐Hui He, John McKay +2 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Number Theory (math.NT) #Representation Theory (math.RT) #hep-th #math.AG #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.1505.06742

49 pages

arxiv created 2015/05/25 · openalex publication_date 2015/05/25 · arxiv updated 2015/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Modular functions arising from some finite groups
• Arithmetic groups and the affine E8 Dynkin diagram
• Exceptional Algebra and Sporadic Groups at c=12

Cited by

• 𝐸₈, the most exceptional group

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