Replicable functions arising from code-lattice VOAs fixed by automorphisms

TL;DR

This paper explores the algebraic structures of codes, lattices, and VOAs, focusing on fixed subobjects under automorphisms, and identifies new replicable functions arising from lattice theta quotients.

Contribution

It introduces a general code theoretic framework for understanding replicable functions from fixed sublattices and VOAs, revealing new connections and characterizations.

Findings

Identified new replicable functions from lattice theta quotients.

Established a code theoretic characterization of order doubling.

Proved decomposition results for characters of fixed subVOAs.

Abstract

We ascertain properties of the algebraic structures in towers of codes, lattices, and vertex operator algebras (VOAs) by studying the associated subobjects fixed by lifts of code automorphisms. In the case of sublattices fixed by subgroups of code automorphisms, we identify replicable functions that occur as quotients of the associated theta functions by suitable eta products. We show that these lattice theta quotients can produce replicable functions not associated to any individual automorphisms. Moreover, we show that the structure of the fixed subcode can induce certain replicable lattice theta quotients and we provide a general code theoretic characterization of order doubling for lifts of code automorphisms to the lattice-VOA. Finally, we prove results on the decompositions of characters of fixed subVOAs.