The Free Generalized Vertex Algebras and Generalized Principal Subspaces

TL;DR

This paper introduces the concept of free generalized vertex algebras linked to non-integral lattices, providing combinatorial bases, character formulas, and applications to describing commutants of principal subspaces.

Contribution

It defines free generalized vertex algebras, establishes their equivalence to generalized principal subspaces, and explores their combinatorial and character properties.

Findings

Established combinatorial bases for free generalized vertex algebras

Derived character formulas for these algebras

Described commutants of principal subspaces using generalized principal subspaces

Abstract

The notion of {\it free} generalized vertex algebras is introduced. It is equivalent to the notion of {\it generalized principal subspaces} associated with lattices which are not necessarily integral. Combinatorial bases and the characters of the free generalized vertex algebras are given. As an application, the commutants of principal subspaces are described by using generalized principal subspaces.