The residual spectrum of an inner form of 𝑆𝑝₈ supported in the minimal parabolic subgroup

Grbac, Neven

doi:10.1090/S0002-9947-09-04853-3

The residual spectrum of an inner form of $Sp_8$ supported in the minimal parabolic subgroup
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Abstract:

The part of the residual spectrum of an inner form of the split group $Sp_8$ supported in the minimal parabolic subgroup is decomposed. Since the considered inner form is not quasi–split, the normalization of the standard intertwining operators, required for the calculation of the poles of the Eisenstein series, is out of the reach of the Langlands–Shahidi method. Hence, a normalization technique, based on the transfer of the Plancherel measure between the split group and its inner form, is applied. The obtained decomposition reveals certain features of the residual spectrum of the inner form which do not appear for the split group.

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