Canonical bases for modified quantum glngln and q-Schur algebras

We will present an elementary algebraic construction of canonical bases for modified quantum glngln and q  -Schur algebras. Furthermore, we will discuss the relation between the canonical basis of the positive part of quantum glngln and the canonical basis of modified quantum glngln. Finally, we will establish an explicit connection between the canonical basis of modified quantum glngln and that of q-Schur algebras.