Vertex-algebraic structure of principal subspaces of standard A_2^{(2)}-modules, I

TL;DR

This paper investigates the vertex-algebraic structure of principal subspaces of standard modules for the twisted affine Kac-Moody algebra A_2^{(2)}, focusing on the basic module as a foundational case for future generalizations.

Contribution

It develops the theory of principal subspaces for A_2^{(2)} and provides a detailed analysis of its basic module, laying groundwork for extension to higher rank algebras.

Findings

Established the structure of principal subspaces for A_2^{(2)}

Analyzed the vertex-algebraic properties of the basic module

Set the stage for future research on higher rank algebras

Abstract

Extending earlier work of the authors, this is the first in a series of papers devoted to the vertex-algebraic structure of principal subspaces of standard modules for twisted affine Kac-Moody algebras. In this part, we develop the necessary theory of principal subspaces for the affine Lie algebra A_2^{(2)}, which we expect can be extended to higher rank algebras. As a "test case," we consider the principal subspace of the basic A_2^{(2)}-module and explore its structure in depth.