Isomeric Heisenberg and Kac-Moody categorification I

TL;DR

This paper introduces a framework for isomeric categorification related to supergroup representations, focusing on Heisenberg and Kac-Moody structures, and explains their interrelation.

Contribution

It develops the first comprehensive approach to isomeric Heisenberg and Kac-Moody categorification in the context of supergroup representation theory.

Findings

Defines isomeric Heisenberg and Kac-Moody categorification

Establishes a method to transition between these categorifications

Lays groundwork for further study in supergroup representation theory

Abstract

We develop a general framework for studying Abelian categories arising in isomeric representation theory, that is, representation theory broadly related to the supergroup Q(n). In this first part, we introduce notions of isomeric Heisenberg categorification and isomeric Kac-Moody categorication, and explain how to pass from the former to the latter. This is analogous to the passage from Heisenberg categorification to Kac-Moody categorification developed in our previous work with Webster.