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2010 Generalized moonshine I: Genus-zero functions
Scott Carnahan
Algebra Number Theory 4(6): 649-679 (2010). DOI: 10.2140/ant.2010.4.649


We introduce a notion of Hecke-monicity for functions on certain moduli spaces associated to torsors of finite groups over elliptic curves, and show that it implies strong invariance properties under linear fractional transformations. Specifically, if a weakly Hecke-monic function has algebraic integer coefficients and a pole at infinity, then it is either a holomorphic genus-zero function invariant under a congruence group or of a certain degenerate type. As a special case, we prove the same conclusion for replicable functions of finite order, which were introduced by Conway and Norton in the context of monstrous moonshine. As an application, we introduce a class of Lie algebras with group actions, and show that the characters derived from them are weakly Hecke-monic. When the Lie algebras come from chiral conformal field theory in a certain sense, then the characters form holomorphic genus-zero functions invariant under a congruence group.


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Scott Carnahan. "Generalized moonshine I: Genus-zero functions." Algebra Number Theory 4 (6) 649 - 679, 2010.


Received: 28 December 2008; Revised: 2 October 2009; Accepted: 5 January 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1236.11041
MathSciNet: MR2728485
Digital Object Identifier: 10.2140/ant.2010.4.649

Rights: Copyright © 2010 Mathematical Sciences Publishers


Vol.4 • No. 6 • 2010
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