  In 1990 Beilinson, Lusztig and MacPherson provided a geometric realization of
modified quantum $\mathfrak{gl}_n$ 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
$\mathfrak{gl}_n$, 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 $\mathfrak{gl}_n$.

Quantum Algebra;Representation Theory