Tensor products of psl(2|2) representations

Abstract

The aim of this work is to study finite dimensional representations of the Lie superalgebra psl(2|2) and their tensor products. In particular, we shall decompose all tensor products involving typical (long) and atypical (short) representations as well as their so-called projective covers. While tensor products of long multiplets and projective covers close among themselves, we shall find an infinite family of new indecomposables in the tensor products of two short multiplets. Our note concludes with a few remarks on possible applications to the construction of AdS_3 backgrounds in string theory.

29 pages

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Cited by in corpus (19)

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• Boundary Spectra in Superspace Sigma-Models
• On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM
• The Sigma Model on Complex Projective Superspaces
• Superspace conformal field theory
• Asymptotic Symmetries of String Theory on AdS3 X S3 with Ramond-Ramond Fluxes
• String States on AdS_3 x S^3 from the Supergroup
• Massless particles on supergroups and AdS3 x S3 supergravity
• On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra
• Secret Symmetries in AdS/CFT
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Branes in JT (super)gravity from group theory
• Edge states and conformal boundary conditions in super spin chains and super sigma models
• Drinfeld realization of the centrally extended $\mathfrak{psl}(2|2)$ Yangian algebra with the manifest coproducts
• Pieri type rules and $GL(2|2)$ tensor products
• Young supertableaux and the large $\mathcal{N}=4$ superconformal algebra
• High-Gradient Operators in the psl(2|2) Gross-Neveu Model