Quasi-particle bases of principal subspaces for the affine Lie algebras of types Bl(1) and Cl(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.