Monomial bases for $q$-Schur algebras
Monomial bases for $q$-Schur algebras
Using the Beilinson-Lusztig-MacPherson construction of the quantized enveloping algebra of $\mathfrak {gl}_n$ and its associated monomial basis, we investigate $q$-Schur algebras $\mathbf {S}_q(n,r)$ as "little quantum groups". We give a presentation for $\mathbf {S}_q(n,r)$ and obtain a new basis for the integral $q$-Schur algebra $S_q(n,r)$, which consists of certain monomials …