Representation theory of sl(2|1)

Abstract

In this note we present a complete analysis of finite dimensional representations of the Lie superalgebra sl(2|1). This includes, in particular, the decomposition of all tensor products into their indecomposable building blocks. Our derivation makes use of a close relation with the representation theory of gl(1|1) for which analogous results are described and derived.

26pp, v2: minor typos corrected

References in corpus (17)

• Type IIB superstring action in AdS_5 x S^5 background
• Conformal Field Theory of AdS Background with Ramond-Ramond Flux
• Superstring Theory on AdS_2 x S^2 as a Coset Supermanifold
• Exact exponents for the spin quantum Hall transition
• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
• Non-unitary Conformal Field Theory and Logarithmic Operators for Disordered Systems
• $PSL(n|n)$ Sigma Model as a Conformal Field Theory
• Conformal Algebras of 2D Disordered Systems
• S and T matrices for the super $U(1,1)$ WZW model. Application to surgery and 3-manifold invariants based on the Alexander Conway polynomial
• The GS String Action on AdS(3)xS(3) with Ramond-Ramond Charge
• Conformal Field Theory at central charge c=0 and Two-Dimensional Critical Systems with Quenched Disorder
• Continuum Limit of the Integrable sl(2/1) 3-\bar{3} Superspin Chain
• Higher-Level Appell Functions, Modular Transformations, and Characters
• Conformal field theory of the integer quantum Hall plateau transition
• The arboreal gas and the supersphere sigma model
• Tensor products of psl(2|2) representations
• Classification of finite dimensional modules of singly atypical type over the Lie superalgebras sl(m/n)

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