  Our goal is to establish what seems to be the first rigidity result for CR
embeddings between Shilov boundaries of bounded symmetric domains of higher
rank. The result states that any such CR embedding is the standard linear
embedding up to CR automorphisms. Our basic assumption extends precisely the
well-known optimal bound for the rank one case. There are no other restrictions
on the ranks, in particular, the difficult case when the target rank is larger
than the source rank is also allowed.
