I'm interested in the theory of Luna and Vust of embeddings of homogenous spaces like presented in
D. Luna, Th. Vust: Plongements d'espaces homogènes, Comment. Math. Helvetici 58 (1983) 186-245.
Especially I'm interested in the case of $SL(2)$ embeddings, which is presented at the end of the paper.
My french isn't very well (sorry my english also...) and it's difficult for me to understand the original paper. Are there other sources for this topic?
https://www.researchgate.net/publication/251217821_General_Theory_of_Embeddings But you have to have an account to see it