Editing Fundamental representation (section)

== Examples ==
* In the case of the [[general linear group]], all fundamental representations are [[exterior product]]s of the defining module. 
* In the case of the special unitary group [[SU(n)|SU(''n'')]], the ''n''&nbsp;&minus;&nbsp;1 fundamental representations are the wedge products <math>\operatorname{Alt}^k\ {\mathbb C}^n</math> consisting of the [[alternating tensor]]s, for ''k''&nbsp;=&nbsp;1,&nbsp;2,&nbsp;...,&nbsp;''n''&nbsp;&minus;&nbsp;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 a Lie group|adjoint representation]] of the simple Lie group of type [[E8 (mathematics)|E<sub>8</sub>]] is a fundamental representation.