The representation dimension of Hecke algebras and symmetric groups

TL;DR

This paper investigates bounds on the representation dimension of classical Hecke algebras of types A, B, D, and certain symmetric group algebras, providing new insights into their algebraic complexity.

Contribution

It establishes lower bounds for all classical Hecke algebras and upper bounds for most type A, B, D algebras, along with bounds for symmetric group algebras, advancing understanding of their representation dimensions.

Findings

Lower bounds for all classical Hecke algebras of types A, B, D.

Upper bounds for most type A, B, D Hecke algebras.

Bounds for the representation dimension of some symmetric group algebras.

Abstract

We establish a lower bound for the representation dimension of all the classical Hecke algebras of types A, B and D. For all the type A algebras, and most of the algebras of types B and D, we also establish upper bounds. Moreover, we establish bounds for the representation dimension of group algebras of some symmetric groups.