# Symmetry breaking for orthogonal groups and a conjecture by B. Gross and D. Prasad

## TL;DR

This paper investigates symmetry breaking in orthogonal groups, confirming conjectures by Gross and Prasad for tempered representations through analysis of H-equivariant homomorphisms between specific unitary representations.

## Contribution

It provides new results verifying Gross and Prasad's conjectures for tempered representations of orthogonal groups, expanding understanding of symmetry breaking phenomena.

## Key findings

- Confirmed conjectures for tempered representations
- Analyzed H-equivariant homomorphisms between specific representations
- Extended results to unitary representations with trivial infinitesimal character

## Abstract

We consider irreducible unitary representations $A_i$ of G=SO(n+1,1) with the same infinitesimal character as the trivial representation and representations $B_j$ of H=SO(n,1) with the same properties and discuss H-equivariant homomorphisms Hom_H($A_i,B_j$). For tempered representations our results confirm the predictions of conjectures by B. Gross and D. Prasad.