Explanation
The irreducible representations of a simply-connected compact Lie group are indexed by their highest weights. These weights are the lattice points in an orthant Q+ 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 combinations of the fundamental weights. 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.
Read more about this topic: Fundamental Representation
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