Blocks of affine quantum Schur algebras

TL;DR

This paper classifies the blocks of affine quantum Schur algebras, which are key in understanding their representation theory and connections to quantum affine gl_n, extending previous classification of irreducible modules.

Contribution

It provides a classification of blocks for affine quantum Schur algebras, a significant step in understanding their module categories.

Findings

Classification of blocks for affine quantum Schur algebras.

Enhanced understanding of their module category structure.

Connections to quantum affine gl_n representations.

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.