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.

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DOI: 10.5802/alco.116
Classification: 05E05, 05E10, 17B69
Keywords: Symmetric Grothendieck polynomials, Boson-fermion correspondence.

Iwao, Shinsuke 1

1 Department of Mathematics, Tokai University, 4-1-1, Kitakaname, Hiratsuka, Kanagawa 259-1292, Japan.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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/articles/10.5802/alco.116/

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