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

The aim of this work is to construct the quasi-particle basis of principal subspace of standard module of highest weight $k{\mathrm{\Lambda }}_0$ of level $k\ge 1$ of affine Lie algebra of type $G_2^{(1)}$ by means of which we obtain the basis of principal subspace of generalized Verma module.