Affine quasi-heredity of affine Schur algebras

TL;DR

This paper proves that affine Schur algebras are affine quasi-hereditary, leading to results on their global dimension, centralizer subquotients, and simple module parametrization, advancing understanding of their algebraic structure.

Contribution

It establishes the affine quasi-heredity of affine Schur algebras, a new structural property with implications for their representation theory.

Findings

Affine Schur algebra $\\whS(n,r)$ is affine quasi-hereditary.

$\\whS(n,r)$ has finite global dimension.

Centralizer subquotients are Laurent polynomial algebras.

Abstract

In this paper we prove that the affine Schur algebra $\whS(n,r)$ is affine quasi-hereditary. This result is then applied to show that $\whS(n,r)$ has finite global dimension and its centralizer subquotient algebras are Laurent polynomial algebras. We also use the result to give a parameter set of simple $\whS(n,r)$-modules and identify this parameter set with that given in \cite{DDF}.