# 2-Verma modules and the Khovanov-Rozansky link homologies

## TL;DR

This paper connects the HOMFLY-PT link polynomial to parabolic Verma modules and extends this framework to categorify Khovanov-Rozansky homology using higher representation theory.

## Contribution

It introduces a novel categorification approach for Khovanov-Rozansky homology via parabolic 2-Verma modules, linking link invariants to higher representation theory.

## Key findings

- HOMFLY-PT polynomial interpreted through parabolic Verma modules
- Categorification of Khovanov-Rozansky homology using 2-Verma modules
- New higher representation theory construction for link homologies

## Abstract

We explain how Queffelec-Sartori's construction of the HOMFLY-PT link polynomial can be interpreted in terms of parabolic Verma modules for $\mathfrak{gl}_{2n}$. Lifting the construction to the world of categorification, we use parabolic 2-Verma modules to give a higher representation theory construction of Khovanov-Rozansky's triply graded link homology.