An orbifold theory of genus zero associated to the sporadic group \(M_{24}\)
type: Item
instance of: scholarly article
title: An orbifold theory of genus zero associated to the sporadic group \(M_{24}\)
zbMATH Open document ID: 0835.20027
DOI: 10.1007/BF02108807
author: Chongying Dong
author: Geoffrey Mason
published in: Communications in Mathematical Physics
publication date: 1994-08-10T00:00:00Z
review text: Let \(\Gamma_{24}\) be the lattice of rank 24 whose root system is of type \(D_{24}\) and let \(V_{\Gamma_{24}}\) be the self-dual bosonic conformal field theory associated with the lattice \(\Gamma_{24}\). In this paper it is proved that if the sporadic simple group \(M_{24}\) is a group of automorphisms of \(V_{\Gamma_{24}}\) then the corresponding orbifold has the genus zero property. That is, each partition function \(Z(g,h,\tau)\) corresponding to commuting pairs \(g\), \(h\) of elements in \(M_{24}\) is either identically zero or a Hauptmodul, i.e., it generates the field of functions on the subgroup of \(\text{SL}_2(\mathbb{R})\) which fixes \(Z(g,h,\tau)\), which then necessarily has genus zero.
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 11F22
Mathematics Subject Classification ID: 81T40
zbMATH DE Number: 617371
zbMATH Keywords: lattice of rank 24
zbMATH Keywords: root systems
zbMATH Keywords: bosonic conformal field theory
zbMATH Keywords: sporadic simple groups
zbMATH Keywords: group of automorphisms
zbMATH Keywords: orbifolds
zbMATH Keywords: genus zero property
zbMATH Keywords: partition functions
reviewed by: Kanat Abdukhalikov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02108807
OpenAlex ID: W1986650240
description: scientific article; zbMATH DE number 617371