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.

Résumé

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.

Détail

Reçu le : 2019-06-07
Révisé le : 2020-02-18
Accepté le : 2020-02-25
Publié le : 2020-10-12

DOI : 10.5802/alco.116

Classification : 05E05, 05E10, 17B69
Keywords: Symmetric Grothendieck polynomials, Boson-fermion correspondence.

Licence : CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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