ALGEBRAIC COMBINATORICS

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.

Revised:
Accepted:
Published online:
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 = {https://alco.centre-mersenne.org/articles/10.5802/alco.116/}
}
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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