# Endomorphism Algebras of Some Modules for Schur Algebras and Representation Dimension

## TL;DR

This paper investigates the representation dimension of Schur algebras, providing bounds in both ordinary and quantum cases, with implications for understanding their module categories.

## Contribution

It establishes lower bounds for the representation dimension of Schur algebras in positive characteristic and upper bounds in the quantum case over characteristic zero fields.

## Key findings

- Lower bounds for representation dimension in positive characteristic
- Upper bounds in the quantum case over characteristic zero
- Insights into module category complexity of Schur algebras

## Abstract

We consider the representation dimension, for fixed $n\geq2$, of ordinary and quantised Schur algebras $S(n,r)$ over a field $k$. For $k$ of positive characteristic $p$ we give a lower bound valid for all $p$. We also give an upper bound in the quantum case, when $k$ has characteristic $0$.