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

Cite this

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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}",

note = "Funding Information: H. Mizukawa was supported by KAKENHI 24740033. H.-F. Yamada was supported by KAKENHI 24540020.",

year = "2014",

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AU - Mizukawa, Hiroshi

AU - Nakajima, Tatsuhiro

AU - Seno, Ryoji

AU - Yamada, Hiro Fumi

N1 - Funding Information: H. Mizukawa was supported by KAKENHI 24740033. H.-F. Yamada was supported by KAKENHI 24540020.

PY - 2014/10

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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

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