S. Carnahan. (2008)cite arxiv:0812.3440
Comment: 23 pages, (v3) all schemes removed, published.
Аннотация
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.
%0 Generic
%1 Carnahan2008
%A Carnahan, Scott
%D 2008
%K genus moonshine zero
%T Generalized Moonshine I: Genus zero functions
%U http://arxiv.org/abs/0812.3440
%X 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.
@misc{Carnahan2008,
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 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.
},
added-at = {2010-10-15T16:13:03.000+0200},
author = {Carnahan, Scott},
biburl = {https://www.bibsonomy.org/bibtex/2a244bf46c08bfae2455beeacb10cbe25/uludag},
description = {Generalized Moonshine I: Genus zero functions},
interhash = {5e8fd6ba5f43f6bd82e7e77fab8eb2c0},
intrahash = {a244bf46c08bfae2455beeacb10cbe25},
keywords = {genus moonshine zero},
note = {cite arxiv:0812.3440
Comment: 23 pages, (v3) all schemes removed, published},
timestamp = {2010-10-15T16:13:03.000+0200},
title = {Generalized Moonshine I: Genus zero functions},
url = {http://arxiv.org/abs/0812.3440},
year = 2008
}