Siegel modular forms for Mathieu moonshine

Abstract: Mathieu moonshine is a correspondence between modular objects and conjugacy classes of the Mathieu group M_24. The most famous one (due to Eguchi-Ooguri-Tachikawa) associates Jacobi forms and mock Modular forms to every conjugacy class of M_24. A second-quantized version of Mathieu moonshine leads to a product formula for functions that are potentially genus-two Siegel Modular Forms analogous to the Igusa Cusp Form. The modularity of these functions do not follow in an obvious manner. We express these product formulae for all conjugacy classes of M_{24} in terms of products of standard modular forms. This provides a new proof of their modularity.

other condensed matterstatistical mechanicsstrongly correlated electronsgeneral relativity and quantum cosmologyHEP - theorymathematical physicsalgebraic geometrydifferential geometrydynamical systemsgroup theorynumber theoryquantum algebrarepresentation theory

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Number theory, Arithmetic and Algebraic Geometry, and Physics

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