Abstract
AbstractLet E/F be a quadratic extension of p–adic fields and let d, m be nonnegative integers of distinct parities. Fix admissible irreducible tempered representations π and σ of GLd(E) and GLm(E) respectively. We assume that π and σ are conjugate–dual. That is to say and where c is the nontrivial F–automorphism of E. This implies that we can extend π to an unitary representation π of a nonconnected group GLd(E) . Define the same way. We state and prove an integral formula for involving the characters of and . ˜˜This formula is related to the local Gan–Gross–Prasad conjecture for unitary groups.
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