Constructs non-vanishing symmetry-breaking operators for branching of discrete series representations of orthogonal groups associated to real hyperboloids.
Symmetry breaking for orthogonal groups and a conjecture by B. Gross and D. Prasad
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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.
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math.RT 1years
2019 1verdicts
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Branching laws for discrete series of some affine symmetric spaces
Constructs non-vanishing symmetry-breaking operators for branching of discrete series representations of orthogonal groups associated to real hyperboloids.