# Representations of centrally extended Lie superalgebra psl(2|2)

## Abstract

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:

- Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3854 CE Utrecht (Netherlands)
- School of Mathematics and Statistics, University of Sydney, NSW 2006 (Australia)

- Publication Date:

- OSTI Identifier:
- 22305870

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics

- Additional Journal Information:
- Journal Volume: 55; Journal Issue: 9; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

- 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

### Citation Formats

```
Matsumoto, Takuya, E-mail: t.matsumoto@uu.nl, and Molev, Alexander, E-mail: alexander.molev@sydney.edu.au.
```*Representations of centrally extended Lie superalgebra psl(2|2)*. United States: N. p., 2014.
Web. doi:10.1063/1.4896396.

```
Matsumoto, Takuya, E-mail: t.matsumoto@uu.nl, & Molev, Alexander, E-mail: alexander.molev@sydney.edu.au.
```*Representations of centrally extended Lie superalgebra psl(2|2)*. United States. doi:10.1063/1.4896396.

```
Matsumoto, Takuya, E-mail: t.matsumoto@uu.nl, and Molev, Alexander, E-mail: alexander.molev@sydney.edu.au. Mon .
"Representations of centrally extended Lie superalgebra psl(2|2)". United States. doi:10.1063/1.4896396.
```

```
@article{osti_22305870,
```

title = {Representations of centrally extended Lie superalgebra psl(2|2)},

author = {Matsumoto, Takuya, E-mail: t.matsumoto@uu.nl and Molev, Alexander, E-mail: alexander.molev@sydney.edu.au},

abstractNote = {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.},

doi = {10.1063/1.4896396},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 9,

volume = 55,

place = {United States},

year = {2014},

month = {9}

}

DOI: 10.1063/1.4896396

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