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Grothendieck polynomials and the Boson-Fermion correspondence

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arxiv 1905.07692 v4 pith:TZICRGN6 submitted 2019-05-19 math.CO math.KT

Shinsuke Iwao This is my paper · ORCID
classification math.COmath.KT
keywords polynomialsboson-fermioncorrespondenceformulasgrothendieckalgebraicalternativecombinatorial
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Colored five-vertex models and Lascoux polynomials and atoms

    math.CO 2019-08 accept novelty 8.0 of 10

    A colored five-vertex model has Lascoux atom and polynomial partition functions, proving the Pechenik-Scrimshaw and Monical set-valued tableau conjectures.

  2. Integrability approach to Feher-Nemethi-Rimanyi-Guo-Sun type identities for factorial Grothendieck polynomials

    math.CO 2019-09 conditional novelty 5.0 of 10

    Using five-vertex model wavefunctions, the author reproves the Guo-Sun identity and proves a new identity and duality for rectangular factorial Grothendieck polynomials.

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