## *Symmetry Breaking for Representations of Rank One Orthogonal
Groups*.
Workshop
on Representations of Lie Groups and their Subgroups (organized by G.
Chang). Chalmers University of Technology, Sweden, 19-20 September 2013.

I begin with the general theory of real spherical varieties
applied to branching problems, and then explain a method
to give a complete classification of breaking symmetry operators
between spherical principal series representations
of *O*(*n*+1,1) and *O*(*n*,1).
A new feature at integral points will be also discussed.
If time allows, I then use the results to determine
the breaking symmetry operators between their irreducible
composition factors.

© Toshiyuki Kobayashi