Brou\'e's abelian defect group conjecture for the sporadic simple Janko group J_4 revisited

TL;DR

This paper proves a Puig equivalence between specific blocks of the Janko group J_4 and the alternating group A_8, using computational methods to advance understanding of modular representation theory.

Contribution

It establishes a Puig equivalence between a 3-block of J_4 and the principal 3-block of A_8, addressing a previously open question.

Findings

Confirmed Puig equivalence between the blocks

Applied explicit Brauer construction computationally

Enhanced understanding of block relationships in sporadic groups

Abstract

We show that the 3-block of the sporadic simple Janko group J_4 with defect group C_3 x C_3, and the principal 3-block of the alternating group A_8 are Puig equivalent, answering a question posed in earlier work of Koshitani-Kunugi-Waki. To accomplish this, we apply computational techniques, in particular an explicit version of the Brauer construction.