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

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

May 14, 2014

27 pages

Published in:

J.Math.Phys. 55 (2014) 091704

Published: 2014

e-Print:

1405.3420 [math.RT]

DOI:

10.1063/1.4896396

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Abstract: (AIP)

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.

Note:

27 pages

Lie superalgebras
Spin chain models
Subspaces
Eigenvalues
Canonical forms

References(17)

Figures(0)

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