Algebraic structure of tensor superoperators for the super-rotation algebra. II

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Abstract
It is shown that the sets of tensor superoperators for the super-rotation algebra can be used to build explicit bases for the representations of several superalgebras. The representations built in this way are the fundamental representations of the special linear superalgebras sl(2j+1‖2j) and of the orthosymplectic superalgebras osp(2j+1‖2j) and the (4j+1)-dimensional representations of osp(1‖2) and sl(1‖2) (Stavraki) superalgebras. It is shown that the chain osp(1‖2)⊆osp(2j+1‖2j) or osp(2j‖2j+1) explains the existence of a series of nontrival zeros for the super-rotation 6-j symbol (SR6-j symbols).

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