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

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
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 9; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
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