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