# Boson-fermion correspondence for Hall-Littlewood polynomials revisited

## TL;DR

This paper explores the relationship between Hall-Littlewood polynomials, vertex operators, and fermionic actions, establishing a boson-fermion correspondence and linking symmetric functions to KP hierarchy tau-functions.

## Contribution

It introduces a new boson-fermion correspondence for Hall-Littlewood polynomials and connects deformed symmetric functions to integrable systems.

## Key findings

- Established a boson-fermion correspondence for Hall-Littlewood polynomials.
- Linked elements orthogonal to Schur functions with KP hierarchy tau-functions.
- Connected twisted vertex operators with classical Heisenberg algebra.

## Abstract

We connect twisted vertex operator presentation of Hall-Littlewood polynomials with the action of charged free fermions, describe a boson-fermion correspondence that relates twisted vertex operators with classical Heisenberg algebra. We also show that the elements of the orthogonal to Schur functions basis of the one-parameter deformation of the ring of symmetric functions $\Lambda[t]$ are $\tau$-functions of KP hierarchy.