# A study of symmetric functions via derived Hall algebra

## TL;DR

This paper explores the connection between symmetric functions and derived Hall algebra, specifically reconstructing the theory of Hall-Littlewood functions through algebraic methods.

## Contribution

It introduces a novel approach using derived Hall algebra of nilpotent Jordan quiver representations to study symmetric functions.

## Key findings

- Reconstruction of Hall-Littlewood symmetric functions from derived Hall algebra
- New operators acting on symmetric functions derived from algebraic structures
- Enhanced understanding of the algebraic foundations of symmetric functions

## Abstract

We use derived Hall algebra of the category of nilpotent representations of Jordan quiver to reconstruct the theory of symmetric functions, focusing on Hall-Littlewood symmetric functions and various operators acting on them.