Abstract
We discuss the classification of strongly regular vertex operator algebras (VOAs) with exactly three simple modules whose character vector satisfies a monic modular linear differential equation with irreducible monodromy. Our main theorem provides a classification of all such VOAs in the form of one infinite family of affine VOAs, one individual affine algebra and two Virasoro algebras, together with a family of eleven exceptional character vectors and associated data that we call the -series. We prove that there are at least VOAs in the -series occurring as commutants in a Schellekens list holomorphic VOA. These include the affine algebra and Höhn’s baby monster VOA but the other seem to be new. The idea in the proof of our main theorem is to exploit properties of a family of vector-valued modular forms with rational functions as Fourier coefficients, which solves a family of modular linear differential equations in terms of generalized hypergeometric series.
Citation
Cameron Franc. Geoffrey Mason. "Classification of some vertex operator algebras of rank 3." Algebra Number Theory 14 (6) 1613 - 1667, 2020. https://doi.org/10.2140/ant.2020.14.1613
Information