Sporadic and Exceptional

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.

49 pages

References in corpus (13)

• Notes on the K3 Surface and the Mathieu group M_24
• Exploring Positive Monad Bundles And A New Heterotic Standard Model
• The Master Space of N=1 Gauge Theories
• N=2 Gauge Theories: Congruence Subgroups, Coset Graphs and Modular Surfaces
• Gauge Theories and Dessins d'Enfants: Beyond the Torus
• Modular Subgroups, Dessins d'Enfants and Elliptic K3 Surfaces
• Kronecker's limit formula, holomorphic modular functions and $q$-expansions on certain moonshine groups
• Exceptional Algebra and Sporadic Groups at c=12
• Eta Products, BPS States and K3 Surfaces
• A modular quintic Calabi-Yau threefold of level 55
• Arithmetic groups and the affine E8 Dynkin diagram
• The algebraic meaning of genus-zero
• "McKay's E7 observation on the Baby Monster" and "McKay's E6 observation on the largest Fischer group"

Cited by in corpus (5)

• The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning
• $E_8$, the most exceptional group
• Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks
• A supersingular coincidence
• Modular curves, invariant theory and $E_8$