Symmetry Breaking for Representations of Rank One Orthogonal Groups II

Chapter 1 Introduction

Chapter 2 Review of Principal Series Representations

Chapter 3 Symmetry Breaking Operators for Principal Series Representations—General Theory

Chapter 4 Symmetry Breaking for Irreducible Representations with Infinitesimal Character ρ

Chapter 5 Regular Symmetry Breaking Operators

Chapter 6 Differential Symmetry Breaking Operators

Chapter 7 Minor Summation Formulæ Related to Exterior Tensor $$\begin{array}{lll}\bigwedge^i\;(\mathbb{C}^n)\end{array}$$

Chapter 9 Regular Symmetry Breaking Operators 𝔸 ˜ λ , ν , δ ε i , j $${\widetilde {\mathbb {A}}}_{{\lambda },{\nu },{\delta \varepsilon }}^{{i,j}}$$ from I δ ( i , λ ) to J ε ( j , ν )

Chapter 10 Symmetry Breaking Operators for Irreducible Representations with Infinitesimal Character ρ : Proof of Theorems4.1 and 4.2

Chapter 11 Application I: Some Conjectures by B. Gross and D. Prasad: Restrictions of Tempered Representations of SO ( n  + 1,  1) to SO ( n ,  1)

Chapter 12 Application II: Periods, Distinguished Representations and ( g , K ) $$(\mathfrak {g},K)$$ -cohomologies

Chapter 13 A Conjecture: Symmetry Breaking for Irreducible Representations with Regular Integral Infinitesimal Character

Chapter 14 Appendix I: Irreducible Representations of G  =  O ( n  + 1, 1), θ -stable Parameters, and Cohomological Induction

Chapter 15 Appendix II: Restriction to G ¯ = S O ( n + 1 , 1 ) $$\overline G=SO(n+1,1)$$

Chapter 16 Appendix III: A Translation Functor for G  =  O ( n  + 1, 1)