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

Journal Article · Mon Sep 15 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4896396· OSTI ID:22305870

Matsumoto, Takuya ^[1]; Molev, Alexander ^[2]

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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)

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.

• OSTI ID: 22305870
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 9; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

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