Quasi-particle bases of principal subspaces for the affine Lie algebras of types $B_{l}^{(1)}$ and $C_{l}^{(1)}$

Abstract

Generalizing our earlier work, we construct quasi-particle bases of principal subspaces of standard module $L_{X_l^{(1)}}(k\Lambda_0)$ and generalized Verma module $N_{X_l^{(1)}}(k\Lambda_0)$ at level $k\geq 1$ in the case of affine Lie algebras of types $B_l^{(1)}$ and $C_l^{(1)}$. As a consequence, from quasi-particle bases, we obtain the graded dimensions of these subspaces.