Quasi-particle bases of principal subspaces of the affine Lie algebra of type $G_2^{(1)}$

TL;DR

This paper constructs a quasi-particle basis for the principal subspace of a standard module of affine Lie algebra of type G2^{(1)}, providing a new combinatorial framework for understanding these algebraic structures.

Contribution

It introduces a novel quasi-particle basis for the principal subspace of G2^{(1)} affine Lie algebra modules, extending previous methods to this specific algebra type.

Findings

Explicit quasi-particle basis constructed for G2^{(1)}

Basis applicable to generalized Verma modules

Enhanced understanding of principal subspace structure

Abstract

The aim of this work is to construct the quasi-particle basis of principal subspace of standard module of highest weight $k\Lambda_0$ of level $k\geq 1$ of affine Lie algebra of type $G_2^{(1)}$ by means of which we obtain the basis of principal subspace of generalized Verma module.