Schur Function Identities Arising From the Basic Representation of A(2)2

Hiroshi Mizukawa, Tatsuhiro Nakajima, Ryoji Seno, Hiro Fumi Yamada

Research output: Contribution to journalArticle

Abstract

A Lie theoretic interpretation is given for some formulas of Schur functions and Schur Q-functions. Two realizations of the basic representation of the Lie algebra A(2)2 are considered; one is on the fermionic Fock space and the other is on the bosonic polynomial space. Via the boson-fermion correspondence, simple relations of the vacuum expectation values of fermions turn out to be algebraic relations of Schur functions.

Original languageEnglish
Pages (from-to)1317-1331
Number of pages15
JournalLetters in Mathematical Physics
Volume104
Issue number10
DOIs
Publication statusPublished - 2014

Fingerprint

Schur Functions
Fermions
Q-function
Fock Space
fermions
Bosons
Lie Algebra
Vacuum
Correspondence
Polynomial
polynomials
algebra
bosons
vacuum
Interpretation

Keywords

  • Boson-fermion correspondence
  • Schur function
  • Schur's Q-function

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Schur Function Identities Arising From the Basic Representation of A(2)2. / Mizukawa, Hiroshi; Nakajima, Tatsuhiro; Seno, Ryoji; Yamada, Hiro Fumi.

In: Letters in Mathematical Physics, Vol. 104, No. 10, 2014, p. 1317-1331.

Research output: Contribution to journalArticle

Mizukawa, Hiroshi ; Nakajima, Tatsuhiro ; Seno, Ryoji ; Yamada, Hiro Fumi. / Schur Function Identities Arising From the Basic Representation of A(2)2. In: Letters in Mathematical Physics. 2014 ; Vol. 104, No. 10. pp. 1317-1331.
@article{e9eed5716a16426d9be6ac324f3d6985,
title = "Schur Function Identities Arising From the Basic Representation of A(2)2",
abstract = "A Lie theoretic interpretation is given for some formulas of Schur functions and Schur Q-functions. Two realizations of the basic representation of the Lie algebra A(2)2 are considered; one is on the fermionic Fock space and the other is on the bosonic polynomial space. Via the boson-fermion correspondence, simple relations of the vacuum expectation values of fermions turn out to be algebraic relations of Schur functions.",
keywords = "Boson-fermion correspondence, Schur function, Schur's Q-function",
author = "Hiroshi Mizukawa and Tatsuhiro Nakajima and Ryoji Seno and Yamada, {Hiro Fumi}",
year = "2014",
doi = "10.1007/s11005-014-0717-y",
language = "English",
volume = "104",
pages = "1317--1331",
journal = "Letters in Mathematical Physics",
issn = "0377-9017",
publisher = "Springer Netherlands",
number = "10",

}

TY - JOUR

T1 - Schur Function Identities Arising From the Basic Representation of A(2)2

AU - Mizukawa, Hiroshi

AU - Nakajima, Tatsuhiro

AU - Seno, Ryoji

AU - Yamada, Hiro Fumi

PY - 2014

Y1 - 2014

N2 - A Lie theoretic interpretation is given for some formulas of Schur functions and Schur Q-functions. Two realizations of the basic representation of the Lie algebra A(2)2 are considered; one is on the fermionic Fock space and the other is on the bosonic polynomial space. Via the boson-fermion correspondence, simple relations of the vacuum expectation values of fermions turn out to be algebraic relations of Schur functions.

AB - A Lie theoretic interpretation is given for some formulas of Schur functions and Schur Q-functions. Two realizations of the basic representation of the Lie algebra A(2)2 are considered; one is on the fermionic Fock space and the other is on the bosonic polynomial space. Via the boson-fermion correspondence, simple relations of the vacuum expectation values of fermions turn out to be algebraic relations of Schur functions.

KW - Boson-fermion correspondence

KW - Schur function

KW - Schur's Q-function

UR - http://www.scopus.com/inward/record.url?scp=84906825197&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84906825197&partnerID=8YFLogxK

U2 - 10.1007/s11005-014-0717-y

DO - 10.1007/s11005-014-0717-y

M3 - Article

VL - 104

SP - 1317

EP - 1331

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 10

ER -