Finite dimensional representations were classified of the orthogonal groups
$ O(p,q) $ were classified by by Hermann Weyl in his famous book ”The classical
groups, their Invariants and Representations ”almost 80 years ago. In this
book he also considered the restriction of a finite dimensional representation
to smaller orthogonal groups and he showed that this restriction can be de-
scribed by his famous branching laws. In this talk I will show that for infinite
dimensional representations of $ O(n,1) $ a very similar branching law describes
the restriction to smaller orthogonal groups although in this case the restric-
tion of the representations is not a direct sum of irreducible representations.
This is joint work with T. Kobayashi.