(2+)-replication and the Baby Monster

TL;DR

This paper introduces the concept of (2+)-replicability for functions related to modular forms and proves that certain McKay-Thompson series associated with the Baby Monster group exhibit this property, expanding understanding of their symmetry structures.

Contribution

The paper defines (2+)-replicability using Hecke operators for (2)^+ and proves that specific McKay-Thompson series for the Baby Monster are completely (2+)-replicable.

Findings

McKay-Thompson series for 2b7 are completely (2+)-replicable

Introduces (2+)-replicability concept linked to Hecke operators for (2)^+

Connects modular functions with Baby Monster group symmetries

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 H\"ohn, are completely $(2+)$-replicable.