Grothendieck polynomials and the boson-fermion correspondence

Shinsuke Iwao

doi:10.5802/alco.116

Grothendieck polynomials and the boson-fermion correspondence

Shinsuke Iwao

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1023-1040
Number of pages	18
Journal	Algebraic Combinatorics
Volume	3
Issue number	5
DOIs	https://doi.org/10.5802/alco.116
Publication status	Published - 2020
Externally published	Yes

Keywords

Boson-fermion correspondence
Symmetric Grothendieck polynomials

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.5802/alco.116

Cite this

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title = "Grothendieck polynomials and the boson-fermion correspondence",

abstract = "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.",

keywords = "Boson-fermion correspondence, Symmetric Grothendieck polynomials",

author = "Shinsuke Iwao",

note = "Funding Information: Keywords. Symmetric Grothendieck polynomials, Boson-fermion correspondence. Acknowledgements. This work is partially supported by JSPS Kakenhi Grant Number 19K03605. Publisher Copyright: {\textcopyright} The journal and the authors, 2020. Some rights reserved.",

year = "2020",

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language = "English",

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AU - Iwao, Shinsuke

N1 - Funding Information: Keywords. Symmetric Grothendieck polynomials, Boson-fermion correspondence. Acknowledgements. This work is partially supported by JSPS Kakenhi Grant Number 19K03605. Publisher Copyright: © The journal and the authors, 2020. Some rights reserved.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Boson-fermion correspondence

KW - Symmetric Grothendieck polynomials

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DO - 10.5802/alco.116

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JO - Algebraic Combinatorics

JF - Algebraic Combinatorics

IS - 5

ER -

Grothendieck polynomials and the boson-fermion correspondence

Abstract

Keywords

ASJC Scopus subject areas

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