Representations of centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$

Abstract

The symmetries provided by representations of the centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$ 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.

arXiv comment27 pages, references added

References in corpus (7)

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• The Yangian symmetry of the Hubbard Model
• Yangians, S-matrices and AdS/CFT
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• Yangian of AdS3/CFT2 and its deformation
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• Drinfeld basis for string-inspired Baxter operators
• Diagonal reduction algebra for $\mathfrak{osp}(1|2)$
• Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction
• Drinfeld realization of the centrally extended $\mathfrak{psl}(2|2)$ Yangian algebra with the manifest coproducts
• Ghost center and representations of the diagonal reduction algebra of $\mathfrak{osp}(1|2)$