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

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

doi:10.1007/s11005-014-0717-y

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

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

Faculty of Science

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

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 language	English
Pages (from-to)	1317-1331
Number of pages	15
Journal	Letters in Mathematical Physics
Volume	104
Issue number	10
DOIs	https://doi.org/10.1007/s11005-014-0717-y
Publication status	Published - Oct 2014

Keywords

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

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s11005-014-0717-y

Fingerprint Dive into the research topics of 'Schur Function Identities Arising From the Basic Representation of A<sup>(2)</sup><sub>2</sub>'. Together they form a unique fingerprint.

Cite this

@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",

month = oct,

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 - 2014/10

Y1 - 2014/10

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

AN - SCOPUS:84906825197

VL - 104

SP - 1317

EP - 1331

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 10

ER -