Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 060, 33 pages      arXiv:1710.01071
Contribution to the Special Issue on Moonshine and String Theory

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

Chris Cummins a and Rodrigo Matias b
a) 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

Received October 04, 2017, in final form May 31, 2018; Published online June 16, 2018

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.

Key words: moonshine; baby monster; replication.

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