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    Representation theory of SU(2) - Wikipedia

    Overview

    In the study of the representation theory of Lie groups, the study of representations of SU(2) is fundamental to the … 展开

    Lie algebra representations

    The representations of the group are found by considering representations of , the Lie algebra of SU(2). Since the group SU(2) is simply connected, every representation of its Lie algebra can be integrated to a group representation; … 展开

    The group representations

    Since SU(2) is simply connected, a general result shows that every representation of its (complexified) Lie algebra gives rise to a representation of SU(2) itself. It is desirable, however, to give an explicit realization of th… 展开

    Another approach

    See under the example for Borel–Weil–Bott theorem. 展开

    Most important irreducible representations and their applications

    Representations of SU(2) describe non-relativistic spin, due to being a double covering of the rotation group of Euclidean 3-space. Relativistic spin is described by the representation theory of SL2(C), a supergroup of S… 展开

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