Essays on representations of real groups The real Jacquet module
نویسنده
چکیده
If (π, V ) is an admissible representation of a p-adic reductive group G and P = MN is a parabolic subgroupwith unipotent radicalN , its Jacquet module VN is the universalN -trivial quotientH0(N,V ) of V by the span of vectors π(n)v − v (n ∈ N ). One fundamental property is that V VN is an exact functor. This construction plays an important role in homomorphisms into representations induced from parabolic subgroups, the asymptotic behaviour of matrix coefficients, formulas for characters, and the classification of admissible representations. It is computed in practice by means of the Bruhat filtration of representations induced from a parabolic subgroup.
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