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In this paper, we give a recursive formula for the interesting PBW basis$E_{A}$ of composition subalgebras of Ringel-Hall algebras $\fkH_\vartri(n)$ ofcyclic quivers after \cite{DengDuXiao2007generic}, and another construction ofcanonical bases of $\U_v^+(\wih{\fks\fkl}_n)$ from the monomial bases $m^{(A)}$follow \cite{DuZhaomultiplication}. As an application, we will determined allthe canonical basis of $\U_v^+(\wih{\fks\fkl}_2)$ associated with modules ofLowery length $\leqs3$. Finally, we will discuss the relation of canonicalbases of Ringel-Hall algebras and those of affine quantum Schur algebras.

Remarks on PBW bases of Ringel-Hall algebras of cyclic quivers