Fundamental representation

Summary

The fundamental representations of a complex semisimple Lie algebra are the irreducible representations whose highest weights are the fundamental weights. There is one for each simple root, so their number is the rank. Every finite-dimensional irreducible representation occurs inside a tensor product of fundamental ones. For $\mathfrak{sl}_n(\C)$ they are the exterior powers $\Lambda^k \C^n$ for $1 \le k \le n - 1$.