Supercategorification of quantum Kac-Moody algebras II

TL;DR

This paper develops a supercategorification framework for quantum Kac-Moody superalgebras using supercategories of supermodules over quiver Hecke superalgebras, extending previous categorification results to the super setting.

Contribution

It introduces a supercategorification of quantum superalgebras and their modules via supercategories of supermodules over quiver Hecke superalgebras, generalizing prior work.

Findings

Supercategories provide a supercategorification of quantum superalgebras.

Specialization yields supercategorification of quantum Kac-Moody superalgebras.

Framework extends categorification to the superalgebra setting.

Abstract

In this paper, we investigate the supercategories consisting of supermodules over quiver Hecke superalgebras and cyclotomic quiver Hecke superalgebras. We prove that these supercategories provide a supercategorification of a certain family of quantum superalgebras and their integrable highest weight modules. We show that, by taking a specialization, we obtain a supercategorification of quantum Kac-Moody superalgebras and their integrable highest weight modules.