Fundamental Representation - Examples

Examples

  • In the case of the general linear group, all fundamental representations are exterior powers of the defining module.
  • In the case of the special unitary group SU(n), the n − 1 fundamental representations are the wedge products consisting of the alternating tensors, for k = 1, 2, ..., n − 1.
  • The spin representation of the twofold cover of an odd orthogonal group, the odd spin group, and the two half-spin representations of the twofold cover of an even orthogonal group, the even spinor group, are fundamental representations that cannot be realized in the space of tensors.
  • The adjoint representation of the simple Lie group of type E8 is a fundamental representation.

Read more about this topic:  Fundamental Representation

Famous quotes containing the word examples:

    “Histories are more full of examples of the fidelity of dogs than of friends.”
    —Alexander Pope (1688–1744)

    “No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
    —André Breton (1896–1966)

    “It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
    —G.C. (Georg Christoph)