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Generalizing our earlier work, we construct quasi-particle bases of principal subspaces of standard module L X (1) l (kΛ 0 ) and generalized Verma module N X (1) l (kΛ 0 ) at level k ≥ 1 in the case of affine Lie algebras of types B(1) l and C (1) l . As a consequence, from quasi-particle bases, we obtain the graded dimensions of these subspaces. IntorductionLet g be a simple complex Lie algebra of type X l , with a Cartan subalgebra h, the set of simple roots Π = {α 1 , . . . , α l } and the triangular decomposition g = n − ⊕ h ⊕ n + , where n + is a direct sum of its one dimensional subalgebras corresponding to the positive roots. Denote by L(n + ) a subalgebra of untwisted affine Lie algebra g of type X(1) lLet V be a highest g-module with highest weight Λ and highest weight vector v Λ . We define the principal subspace W V of V asIn this paper we study principal subspaces of the generalized Verma module N X (1) l (kΛ 0 ) and its irreducible quotient L X (1) l (kΛ 0 ) at level k ≥ 1, defined over the affine Lie algebras of type B(1) l and C(1) l . The study of principal subspaces of standard (i.e., integrable highest weight) modules of the simply laced affine Lie algebras and its connection to Rogers-Ramanujan identities was initiated in the work of B. L. Feigin and A. V. Stoyanovsky [FS] and has been further developed in [AKS]

The aim of this work is to construct the quasi-particle basis of principal subspace of standard module of highest weight kΛ 0 of level k ≥ 1 of affine Lie algebra of type G (1) 2 by means of which we obtain the basis of principal subspace of generalized Verma module. 2010 Mathematics Subject Classification. 17B67, 17B69, 05A19. Key words and phrases. Affine Lie algebras, vertex operator algebras, principal subspaces, quasi-particle bases. This work has been supported in part by the Croatian Science Foundation under the project 2634., by the Croatian Scientific Centre of Excellence QuantiXLie and by University of Rijeka research grant 13.14.1.2.02.

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