Blocks of affine quantum Schur algebras

Abstract: The affine quantum Schur algebra is a certain important infinite dimensional algebra whose representation theory is closely related to that of quantum affine $\frak{gl}n$. Finite dimensional irreducible modules for the affine quantum Schur algebra ${\mathcal S}{\vartriangle}(n,r){v}$ were classified in \cite{DDF}, where $v\in{\mathbb C}^*$ is not a root of unity. We will classify blocks of the affine quantum Schur algebra ${\mathcal S}{\vartriangle}(n,r)_{v}$ in this paper.