TITLE: Where can I find explicit descriptions of principal $SL(2,\mathbb{C})$s?
QUESTION [7 upvotes]: I am interested in an explicit description of the principal homomorphism from $SL(2,\mathbb{C})$ to $G$, for each complex semisimple Lie group $G$. Does any one have specific references please? Kostant's original paper is of course great, and contains a lot, but I do not think it contains explicit descriptions for each specific example (which is what I really want at the moment).

REPLY [2 votes]: I would like to add to the suggested references, one more:
A.L. Onishchik, E.B. Vinberg, Lie Groups and Algebraic Groups,
Springer, 1990. Exercise 4.2.28.