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.

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.