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Constant term of smooth $H_\psi $-spherical functions on a reductive $p$-adic group

2009
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Transactions of the American Mathematical Society
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Let ψ be a smooth character of a closed subgroup, H, of a reductive p-adic group G. If P is a parabolic subgroup of G such that P H is open in G, we define the constant term of every smooth function on G which transforms by ψ under the right action of G. The example of mixed models is given: it includes symmetric spaces and Whittaker models. In this case a notion of cuspidal function is defined and studied. It leads to finiteness theorems. Example 1 (Symmetric spaces). The group H is the fixed

doi:10.1090/s0002-9947-09-04925-3
fatcat:f2kth2rfwbg2jdazcdsam3uaxq