Super-moonshine for Conway’s Largest Sporadic Group
نویسنده
چکیده
We study a self-dual N = 1 super vertex operator algebra, denoted A, and prove that the full symmetry group is Conway’s largest sporadic simple group Co1. We verify a uniqueness result for A which is analogous to that conjectured to characterize the Moonshine vertex operator algebra V . The action of Co1 on A is sufficiently transparent that one can derive explicit expressions for the McKay-Thompson series associated to any automorphism of A. A corollary of the construction is that Co0 (the perfect double cover of Co1) may be characterized as a point-stabilizer in a spin module for Spin24(R).
منابع مشابه
Arithmetic groups and the affine E8 Dynkin diagram
Several decades ago, John McKay suggested a correspondence between nodes of the affine E8 Dynkin diagram and certain conjugacy classes in the Monster group. Thanks to Monstrous Moonshine, this correspondence can be recast as an assignment of discrete subgroups of PSL2(R) to nodes of the affine E8 Dynkin diagram. The purpose of this article is to give an explanation for this latter correspondenc...
متن کاملProof of the umbral moonshine conjecture
The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay–Thompson series are certain distinguished mock modular forms. Gannon has proved this for the special case involving the largest sporadic simple Mathieu group. Here, we establish the existence of the umbral moonshine modules in the remaining 22 cases. Mathematics ...
متن کاملMonstrous Moonshine and Monstrous Lie Superalgebras
Invent. Math. 109, 405-444 (1992). Richard E. Borcherds, Department of pure mathematics and mathematical statistics, 16 Mill Lane, Cambridge CB2 1SB, England. We prove Conway and Norton’s moonshine conjectures for the infinite dimensional representation of the monster simple group constructed by Frenkel, Lepowsky and Meurman. To do this we use the no-ghost theorem from string theory to construc...
متن کاملProblems in moonshine
The talk at the I.C.C.M. was an introduction to moonshine. As there are already several survey articles on what is known about moonshine ([B94], [B99], [D-M94], [DM96], [F-H98], [J]), this paper differs from the talk and will concentrate mainly on what we do not know about it. Moonshine is not a well defined term, but everyone in the area recognizes it when they see it. Roughly speaking, it mea...
متن کاملar X iv : m at h / 06 09 44 9 v 1 [ m at h . R T ] 1 5 Se p 20 06 Moonshine for Rudvalis ’ s sporadic group I ∗
We introduce the notion of vertex operator superalgebra with enhanced conformal structure, which is a refinement of the notion of vertex operator superalgebra. We exhibit several examples, including a particular one which is self-dual, and whose full symmetry group is a direct product of a cyclic group of order seven with the sporadic simple group of Rudvalis. We thus obtain an analogue of Mons...
متن کامل