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.

27 pages, references added

References in corpus (2)

• Yangians, S-matrices and AdS/CFT
• Note on Centrally Extended su(2/2) and Serre Relations

Cited by in corpus (4)

• Drinfeld basis for string-inspired Baxter operators
• 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 $\mathfrak{osp}(1|2)$