Jacquet module

In mathematics, the Jacquet module J(V) of a linear representation V of a group N is the space of co-invariants of N; or in other words the largest quotient of V on which N acts trivially, or the zeroth homology group H₀(N,V). The Jacquet functor J is the functor taking V to its Jacquet module J(V). Use of the phrase "Jacquet module" often implies that V is an admissible representation of a reductive algebraic group G over a local field, and N is the unipotent radical of a parabolic subgroup of G. In the case of p-adic groups they were studied by Jacquet (1971).