Grothendieck polynomials and the Boson-Fermion correspondence

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.

19 pages

References in corpus (1)

• Universal factorial Schur $P,Q$-functions and their duals

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