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

### Takuya Matsumoto and Alexander Molev

#### 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.

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 Friday, May 16, 2014