Monstrous and Generalized Moonshine and Permutation Orbifolds

On the Relationship between Monstrous Moonshine and the Uniqueness of the Moonshine Module

We consider the relationship between the conjectured uniqueness of the Moonshine Module, V♮, and Monstrous Moonshine, the genus zero property of the modular invariance group for each Monster group Thompson series. We first discuss a family of possible Zn meromorphic orbifold constructions of V♮ based on automorphisms of the Leech lattice compactified bosonic string. We reproduce the Thompson se...

06 9 v 1 1 6 N ov 1 99 2 DIAS - STP - 92 - 29 MONSTROUS MOONSHINE AND THE UNIQUENESS OF THE MOONSHINE MODULE

In this talk we consider the relationship between the conjectured uniqueness of the Moonshine module V of Frenkel, Lepowsky and Meurman and Monstrous Moonshine, the genus zero property for Thompson series discovered by Conway and Norton. We discuss some evidence to support the uniqueness of V by considering possible alternative orbifold constructions of V from a Leech lattice compactified strin...

Kac-moody Algebras, the Monstrous Moonshine, Jacobi Forms and Infinite Products

Rademacher sums, Moonshine and Gravity

In 1939 Rademacher demonstrated how to express Klein’s modular invariant as a sum over elements of the modular group. In this article we generalize Rademacher’s approach so as to construct bases for the spaces of automorphic integrals of arbitrary even integer weight, for an arbitrary group commensurable with the modular group. Our methods provide explicit expressions for the Fourier expansions...

Monstrous 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...