Grothendieck polynomials and the boson-fermion correspondence
Algebraic Combinatorics, Volume 3 (2020) no. 5, pp. 1023-1040.

In this paper we study algebraic and combinatorial properties of symmetric 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.

Received: 2019-06-07
Revised: 2020-02-18
Accepted: 2020-02-25
Published online: 2020-10-12
DOI: https://doi.org/10.5802/alco.116
Classification: 05E05,  05E10,  17B69
Keywords: Symmetric Grothendieck polynomials, Boson-fermion correspondence.
@article{ALCO_2020__3_5_1023_0,
     author = {Iwao, Shinsuke},
     title = {Grothendieck polynomials and~the~boson-fermion correspondence},
     journal = {Algebraic Combinatorics},
     pages = {1023--1040},
     publisher = {MathOA foundation},
     volume = {3},
     number = {5},
     year = {2020},
     doi = {10.5802/alco.116},
     language = {en},
     url = {alco.centre-mersenne.org/item/ALCO_2020__3_5_1023_0/}
}
Iwao, Shinsuke. Grothendieck polynomials and the boson-fermion correspondence. Algebraic Combinatorics, Volume 3 (2020) no. 5, pp. 1023-1040. doi : 10.5802/alco.116. https://alco.centre-mersenne.org/item/ALCO_2020__3_5_1023_0/

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