I have come across the terms "basic representation" of a semisimple Lie algebra, but I am finding it hard to find a clear definition of this representation. Can someone provide me a reference or explain to me what this concept is?
- How is the "basic representation" of a (say simple) Lie algebra $\mathfrak{g}$ defined?
- This is supposedly a highest weight representation. What highest weight does this correspond to? Is there a formula or a list I can refer to get these highest weights?
- How do these formulas/definition generalize to Kac-moody Lie algebras?