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.

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