Hyperbolic spaces, principal series, and O(2, infinity)

摘要

We prove that there exists no irreducible representation of the identity component of the isometry group PO(1, n) of the real hyperbolic space of dimension n into the group O(2, infinity) if n >= 3. This is motivated by the existence of irreducible representations (arising from the spherical principal series) of PO(1, n)circle into the groups O(p, infinity) for other values of p.