The local Gan-Gross-Prasad conjecture

in terms of the Langlands parametrization of Irr(G). More precisely, the Gan-Gross-Prasad triples come from certain pairs W ⊂ V of quadratic spaces or hermitian spaces (over a fixed quadratic extension E/F ). We will denote uniformly by h the underlying quadratic or hermitian form on these spaces. To get a GGP triple, you need the following two conditions to be satisfied : – W⊥ (the orthogonal complement of W in V ) is odd-dimensional ; – The orthogonal/unitary group of W⊥ is quasi-plit. Actually, for hermitian spaces the second condition is automatic (i.e. the unitary group of an odd-dimensional hermitian space ove a p-adic field is always quasi-split). In any case, the two above conditions taken together are equivalent to the existence of a basis