An elementary construction of monomial bases of modified quantum affine gl_n

In 1990 Beilinson, Lusztig and MacPherson provided a geometric realization of modified quantum gln and its canonical basis. A key step of their work is a construction of a monomial basis. Recently, Du and Fu provided an algebraic construction of the canonical basis for modified quantum affine gln, which among other results used an earlier construction of monomial bases using Ringel-Hall algebra of the cyclic quiver. In this paper, we give an elementary algebraic construction of a monomial basis for affine Schur algebras and modified quantum affine gln.