Principal subspaces for quantum affine algebra Uq(An(1))

We consider principal subspace W(Λ)W(Λ) of integrable highest weight module L(Λ)L(Λ) for quantum affine algebra Uq(slˆn+1). We introduce quantum analogues of the quasi-particles associated with the principal subspaces for slˆn+1 and discover certain relations among them. By using these relations we find, for certain highest weight Λ  , combinatorial bases of principal subspace W(Λ)W(Λ) in terms of monomials of quantum quasi-particles.