On 2-Verma modules for quantum $\mathfrak{sl}_2$

TL;DR

This paper investigates a superalgebra related to quantum rak{sl}_2, establishing a uniqueness result for 2-Verma modules in a categorification context, expanding understanding of algebraic structures in quantum representation theory.

Contribution

It introduces and studies the superalgebra A_n, demonstrating its properties and proving a uniqueness theorem for 2-Verma modules in rak{sl}_2 categorification.

Findings

Superalgebra A_n shares properties with nilHecke algebra.

Proved a uniqueness result for 2-Verma modules.

Advances categorification of quantum rak{sl}_2 modules.

Abstract

In this paper we study the superalgebra $A_n$, introduced by the authors in previous work on categorification of Verma modules for quantum $\mathfrak{sl}_2$. The superalgebra $A_n$ is akin to the nilHecke algebra, and shares similar properties. In particular, we prove a uniqueness result about 2-Verma modules on $\Bbbk$-linear 2-categories.