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

Abstract

The symmetries provided by representations of the centrally extended Lie superalgebra \documentclass[12pt]{minimal}\begin{document}$\mathfrak {psl}(2|2)$\end{document}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.