59 citations · 221 across the 13 of their papers we have counts for
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Why do the symmetries of the monster vertex algebra form a finite simple group?
Scott Carnahan
Together with their 1988 construction of the monster vertex algebra , Frenkel, Lepowsky, and Meurman showed that the largest sporadic simple group, known as the Fischer…
Monstrous Moonshine for integral group rings
Scott Carnahan, Satoru Urano
We propose a conjecture that is a substantial generalization of the genus zero assertions in both Monstrous Moonshine and Modular Moonshine. Our conjecture essentially asserts that…
Monstrous Moonshine over Z?
Scott Carnahan
Monstrous Moonshine was extended in two complementary directions during the 1980s and 1990s, giving rise to Norton's Generalized Moonshine conjecture and Ryba's Modular Moonshine c…
Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions
Scott Carnahan, Takahiro Komuro, Satoru Urano
Given a holomorphic -cofinite vertex operator algebra with graded dimension , Borcherds's proof of the monstrous moonshine conjecture implies any finite order autom…
A Self-Dual Integral Form of the Moonshine Module
Scott Carnahan
We construct a self-dual integral form of the moonshine vertex operator algebra, and show that it has symmetries given by the Fischer-Griess monster simple group. The existence of…
51 constructions of the Moonshine module
Scott Carnahan
We show using Borcherds products that for any fixed-point free automorphism of the Leech lattice satisfying a "no massless states" condition, the corresponding cyclic orbifold of t…
Fricke Lie algebras and the genus zero property in Moonshine
Scott Carnahan
We give a new, simpler proof that the canonical actions of finite groups on Fricke-type Monstrous Lie algebras yield genus zero functions in Generalized Monstrous Moonshine, using…
Regularity of fixed-point vertex operator subalgebras
Scott Carnahan, Masahiko Miyamoto
We show that if is a simple non-negatively graded regular vertex operator algebra with a nonsingular invariant bilinear form and is a finite order automorphism of , then…
Building vertex algebras from parts
Scott Carnahan
Given a collection of modules of a vertex algebra parametrized by an abelian group, together with one dimensional spaces of composable intertwining operators, we assign a canonical…
Generalized Moonshine IV: Monstrous Lie algebras
Scott Carnahan
For each element of the Fischer-Griess Monster sporadic simple group, we construct an infinite dimensional Lie algebra equipped with a projective action of the centralizer of that…
Generalized moonshine II: Borcherds products
Scott Carnahan
The goal of this paper is to construct infinite dimensional Lie algebras using infinite product identities, and to use these Lie algebras to reduce the generalized moonshine conjec…
Generalized Moonshine I: Genus zero functions
Scott Carnahan
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 invarian…