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Title: Representations of centrally extended Lie superalgebra psl(2|2)

Abstract

The symmetries provided by representations of the centrally extended Lie superalgebra psl(2|2) are known to play an important role in the spin chain models originated in the planar anti-de Sitter/conformal field theory correspondence and one-dimensional Hubbard model. We give a complete description of finite-dimensional irreducible representations of this superalgebra thus extending the work of Beisert which deals with a generic family of representations. Our description includes a new class of modules with degenerate eigenvalues of the central elements. Moreover, we construct explicit bases in all irreducible representations by applying the techniques of Mickelsson–Zhelobenko algebras.

Authors:
 [1];  [2]
  1. Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3854 CE Utrecht (Netherlands)
  2. School of Mathematics and Statistics, University of Sydney, NSW 2006 (Australia)
Publication Date:
OSTI Identifier:
22305870
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 55; Journal Issue: 9; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; ANTI DE SITTER GROUP; ANTI DE SITTER SPACE; CONFORMAL INVARIANCE; EIGENVALUES; GRADED LIE GROUPS; HUBBARD MODEL; IRREDUCIBLE REPRESENTATIONS; QUANTUM FIELD THEORY; SPIN

Citation Formats

Matsumoto, Takuya, E-mail: t.matsumoto@uu.nl, and Molev, Alexander, E-mail: alexander.molev@sydney.edu.au. Representations of centrally extended Lie superalgebra psl(2|2). United States: N. p., 2014. Web. doi:10.1063/1.4896396.
Matsumoto, Takuya, E-mail: t.matsumoto@uu.nl, & Molev, Alexander, E-mail: alexander.molev@sydney.edu.au. Representations of centrally extended Lie superalgebra psl(2|2). United States. doi:10.1063/1.4896396.
Matsumoto, Takuya, E-mail: t.matsumoto@uu.nl, and Molev, Alexander, E-mail: alexander.molev@sydney.edu.au. Mon . "Representations of centrally extended Lie superalgebra psl(2|2)". United States. doi:10.1063/1.4896396.
@article{osti_22305870,
title = {Representations of centrally extended Lie superalgebra psl(2|2)},
author = {Matsumoto, Takuya, E-mail: t.matsumoto@uu.nl and Molev, Alexander, E-mail: alexander.molev@sydney.edu.au},
abstractNote = {The symmetries provided by representations of the centrally extended Lie superalgebra psl(2|2) are known to play an important role in the spin chain models originated in the planar anti-de Sitter/conformal field theory correspondence and one-dimensional Hubbard model. We give a complete description of finite-dimensional irreducible representations of this superalgebra thus extending the work of Beisert which deals with a generic family of representations. Our description includes a new class of modules with degenerate eigenvalues of the central elements. Moreover, we construct explicit bases in all irreducible representations by applying the techniques of Mickelsson–Zhelobenko algebras.},
doi = {10.1063/1.4896396},
journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 9,
volume = 55,
place = {United States},
year = {2014},
month = {9}
}