# Grothendieck polynomials and the Boson-Fermion correspondence

## TL;DR

This paper explores the algebraic and combinatorial aspects of Grothendieck polynomials using the Boson-Fermion correspondence, providing new proofs and insights into their structure and formulas.

## Contribution

It introduces free-fermionic expressions for Grothendieck polynomials, offering novel proofs of determinantal and Pieri formulas.

## Key findings

- Grothendieck polynomials expressed as vacuum expectation values
- Alternative proofs of determinantal formulas
- New derivations of Pieri type formulas

## Abstract

In this paper we study algebraic and combinatorial properties of Grothendieck polynomials and their dual polynomials by means of the Boson-Fermion correspondence. We show that these symmetric functions can be expressed as a vacuum expectation value of some operator that is written in terms of free-fermions. By using the free-fermionic expressions, we obtain alternative proofs of determinantal formulas and Pieri type formulas.

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Source: https://tomesphere.com/paper/1905.07692