On the Malle-Navarro Conjecture for 2- and 3-blocks of general linear and unitary groups

TL;DR

This paper proves the Malle-Navarro conjecture for specific blocks of general linear and unitary groups, advancing understanding of block invariants in modular representation theory.

Contribution

It establishes the conjecture for 2-blocks and unipotent 3-blocks of general linear and unitary groups, including certain quotient groups.

Findings

Proved the conjecture for 2-blocks of general linear and unitary groups.

Confirmed the conjecture for unipotent 3-blocks of these groups.

Extended results to quotients of central subgroups.

Abstract

The Malle-Navarro conjecture relates central block theoretic invariants in two inequalities. In this paper, we prove the conjecture for the 2-blocks and the unipotent 3-blocks of the general linear and unitary groups in non-defining characteristic. Moreover, we show that the conjecture holds for the unipotent 3-blocks of quotients of central subgroups of the special linear and unitary groups.