TITLE: The conformal group of $S^n$.
QUESTION [12 upvotes]: Is there any explicit computation of Conf($S^n$, $g_{std}$), the group of conformal diffeomorphisms of the standard $n$-sphere?

REPLY [4 votes]: Try the book A Mathematical Introduction to Conformal Field Theory by Martin Schottenloher. Chapters 1 and 2 go over some of the proofs you are looking for and the book is example driven.