Wild blocks of type $A$ Hecke algebras are strictly wild

TL;DR

This paper proves that all wild blocks of type A Hecke algebras with quantum characteristic at least 3 are strictly wild, significantly advancing the understanding of their representation theory.

Contribution

It establishes the strict wildness of all wild blocks of type A Hecke algebras with quantum characteristic e ≥ 3, except possibly one specific case.

Findings

All wild blocks with e ≥ 3 are strictly wild.

Wild blocks of q-Schur algebras are also strictly wild for e ≥ 3.

Potential exception for weight 2 Rouquier block at e=3.

Abstract

We prove that all wild blocks of type $A$ Hecke algebras with quantum characteristic $e \geqslant 3$ -- i.e. blocks of weight at least $2$ -- are strictly wild, with the possible exception of the weight $2$ Rouquier block for $e = 3$. As a corollary, we show that for $e \geqslant 3$, all wild blocks of the $q$-Schur algebras are strictly wild, without exception.