We consider principal subspace W({ \Lambda}) of integrable highest weight module L({ \Lambda}) for quantum affine algebra $U_q(\hat{ \mathfrak{ sl}}_{ n+1})$. We introduce quantum analogues of the quasi-particles associated with the principal subspaces for $\hat{ \mathfrak{ sl}}_{ n+1}$ and discover certain relations among them. By using these relations we find, for certain highest weight { \Lambda}, combinatorial bases of principal subspace W({ \Lambda}) in terms of monomials of quantum quasi-particles.
Categories: math.QA