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

SIGMA 14 (2018), 060, 33 pages      arXiv:1710.01071      https://doi.org/10.3842/SIGMA.2018.060
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

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.

Key words: moonshine; baby monster; replication.

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