Highest weight categories arising from Khovanov's diagram algebra IV: the general linear supergroup

TL;DR

This paper establishes a Morita equivalence between blocks of the general linear supergroup and a limit of Khovanov's diagram algebra, demonstrating their Koszul property and deepening the algebraic understanding of supergroups.

Contribution

It introduces a new Morita equivalence linking supergroup blocks to Khovanov's diagram algebra, revealing their Koszul nature.

Findings

Blocks of the general linear supergroup are Morita equivalent to a limiting Khovanov diagram algebra.

Blocks of the supergroup are proven to be Koszul.

The work extends the algebraic framework connecting supergroups and diagram algebras.

Abstract

We prove that blocks of the general linear supergroup are Morita equivalent to a limiting version of Khovanov's diagram algebra. We deduce that blocks of the general linear supergroup are Koszul.