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