Extending results of [Kaz86] to the relative case, we relate harmonic analysis over some spherical spaces , where is a field of positive characteristic, to harmonic analysis over the spherical spaces , where is a suitably chosen field of characteristic 0.
We apply our results to show that the pair is a strong Gelfand pair for all local fields of arbitrary characteristic, and that the pair is a Gelfand pair for local fields of any characteristic different from 2. We also give a criterion for finite generation of the space of -invariant compactly supported functions on as a module over the Hecke algebra.
Cite this article
Avraham Aizenbud, Nir Avni, Dmitry Gourevitch, Spherical pairs over close local fields. Comment. Math. Helv. 87 (2012), no. 4, pp. 929–962DOI 10.4171/CMH/274