Moonshine modules and a question of Griess

JOURNAL OF ALGEBRA

卷:536

Article

Aricheta, Victor Manuel^1,2  Beneish, Lea¹ 

[1] Emory Univ, Dept Math, Atlanta, GA 30322 USA

[2] Univ Philippines, Inst Math, Diliman 1101, Quezon City, Philippines

关键词: Modular forms;    Moonshine;    Representations of sporadic simple groups;    Vertex operator algebras;   

DOI  :  10.1016/j.jalgebra.2019.06.039

来源: Elsevier

【 摘 要 】

We consider the situation in which a finite group acts on an infinite-dimensional graded module in such a way that the graded trace functions are weakly holomorphic modular forms. Under a mild hypothesis we completely describe the asymptotic module structure of the homogeneous subspaces. As a consequence we find that moonshine for a group gives rise to partial orderings on its irreducible representations. This serves as a first answer to a question posed by Griess. In particular, we show that our hypothesis holds for umbral moonshine and for automorphism groups of certain vertex operator algebras. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free