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Representations of the double covers of these teams yield double-valued projective representations of the groups themselves. From a geometrical point of view, one can explicitly assemble the spinors after which look at how they behave under the motion of the related Lie teams. This latter method has the advantage of providing a concrete and elementary description of what a spinor is. Nonetheless, such a description turns into unwieldy when difficult properties of the spinors, such as Fierz ident...
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