On a Pairing of Goldberg-shahidi for Even Orthogonal Groups
نویسنده
چکیده
Let π ⊗ σ be a supercuspidal representation of GL(2n)× SO(2n) over a p-adic field with π selfdual, where SO(2n) stands for a quasisplit even special orthogonal group. In order to study its normalized parabolic induction to SO(6n), Goldberg and Shahidi defined a pairing R between the matrix coefficients of π and σ which controls the residue of the standard intertwining operator. The elliptic part Rell of R is conjectured to be related to twisted endoscopic transfer. Based on Arthur’s endoscopic classification and Spallone’s improvement of Goldberg-Shahidi program, we will verify some of their predictions for general n, under the assumption that π does not come from SO(2n+ 1).
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