Editing Fundamental representation (section)

== Explanation ==

The [[Irreducible representation | irreducible representations]] of a [[simply-connected]] [[compact group| compact]] [[Lie group]] are indexed by their highest [[weight (representation theory)|weights]]. These weights are the lattice points in an orthant ''Q''<sub>+</sub> in the [[weight lattice]] of the Lie group consisting of the dominant integral weights. It can be proved
that there exists a set of ''fundamental weights'', indexed by the vertices of the [[Dynkin diagram]], such that any dominant integral weight is a non-negative integer linear combination of the fundamental weights.<ref>{{harvnb|Hall|2015}} Proposition 8.35</ref> The corresponding irreducible representations are the '''fundamental representations''' of the Lie group. From the expansion of a dominant weight in terms of the fundamental weights one can take a corresponding tensor product of the fundamental representations and extract one copy of the irreducible representation corresponding to that dominant weight.<ref>{{harvnb|Hall|2015}} See the proof of Proposition 6.17 in the case of SU(3)</ref>