Spherical Pairs Over Close Local Fields

Details Spherical Pairs Over Close Local Fields Spherical Pairs Over Close Local Fields

2009-10-16

arxiv.org/abs/0910.3199v3

Mathematics

Representation Theory

v2. Section 2 changed. v3. A change in the definition of uniform spherical pair, which also caused some changes in the formula

Scientific paper

Extending results of Kazhdan to the relative case, we relate harmonic analysis over some spherical spaces G(F)/H(F), where F is a field of positive characteristic, to harmonic analysis over the spherical spaces G(E)/H(E), where E is a suitably chosen field of characteristic 0. One of the Ingredients of the proof is a condition for finite generation of some modules over the Hecke algebra. We apply our results to show that the pair (GL_{n+1},GL_n) is a strong Gelfand pair for all local fields, and that the pair (GL_{n+k},GL_n x GL_k) is a Gelfand pair for all local fields of odd characteristic.

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