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$(2+)$-Replication and the Baby Monster

Chris Cummins^a, Rodrigo Matias<sup>b

a</sup> Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd Ouest, Montréal, H3G 1M8, Québec, Canada
^b Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, Portugal

Abstract: The definitions of replicable and completely replicable functions are intimately related to the Hecke operators for the modular group. We define the notions of "$(2+)$-replicable" and "completely $(2+)$-replicable" functions by considering the Hecke operators for $\Gamma_0(2)^+$. We prove that the McKay–Thompson series for $2\cdot\mathbb{B}$, as computed by Höhn, are completely $(2+)$-replicable.

Keywords: moonshine; baby monster; replication.

MSC: 11F22; 11F25

Received: October 4, 2017; in final form May 31, 2018; Published online June 16, 2018

Language: English

DOI: 10.3842/SIGMA.2018.060

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