A note on principal subspaces of the affine Lie algebras in types $B_l^{(1)}$, $C_l^{(1)}$, $F_4^{(1)}$ and $G_2^{(1)}$

Abstract

We construct quasi-particle bases of principal subspaces of standard modules $L(\Lambda )$, where $\Lambda =k_0{\Lambda }_0+k_j{\Lambda }_j$, and ${\Lambda }_j$ denotes the fundamental weight of affine Lie algebras of type $B_l^{(1)}$, $C_l^{(1)}$, $F_4^{(1)}$ or $G_2^{(1)}$ of level one. From the given bases we find characters of principal subspaces.