Grothendieck polynomials and the boson-fermion correspondence
Iwao, Shinsuke1
1 Department of Mathematics, Tokai University, 4-1-1, Kitakaname, Hiratsuka, Kanagawa 259-1292, Japan.
Algebraic Combinatorics, Tome 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
Mots-clés : Symmetric Grothendieck polynomials, Boson-fermion correspondence.
Iwao, Shinsuke 1

1 Department of Mathematics, Tokai University, 4-1-1, Kitakaname, Hiratsuka, Kanagawa 259-1292, Japan. 
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Iwao, Shinsuke. Grothendieck polynomials and the boson-fermion correspondence. Algebraic Combinatorics, Tome 3 (2020) no. 5, pp. 1023-1040. doi : 10.5802/alco.116. http://www.numdam.org/articles/10.5802/alco.116/

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