2008/12/31 by Scott Carnahan · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #math.NT #math.RT #msc:11F22 #msc:17B69 #msc:20D08
paper · pdf · doi:10.2140/ant.2010.4.649
published as Algebra and Number Theory 4:6 (2010) 649-679 · 23 pages, (v3) all schemes removed, published
openalex publication_date 2010/09/25 · arxiv created 2010/10/14 · arxiv updated 2010/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract. 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 genus zero function 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 Hecke-monic. When the Lie algebras come from chiral conformal