Blocks for general linear supergroup $GL(m|n)$

TL;DR

This paper establishes the linkage principle and characterizes the blocks of the general linear supergroups $GL(m|n)$ over a field of characteristic not equal to 2, advancing understanding of their representation theory.

Contribution

It introduces the linkage principle and describes the block structure of $GL(m|n)$ supergroups in characteristic $p eq 2$, which was previously not well-understood.

Findings

Proved the linkage principle for $GL(m|n)$ supergroups.

Described the block decomposition of the category of representations.

Enhanced understanding of representation theory in positive characteristic.

Abstract

We prove the linkage principle and describe blocks of the general linear supergroups $GL(m|n)$ over the ground field $K$ of characteristic $p\neq 2$.