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).

References

Casselman, W. (1980), "Jacquet modules for real reductive groups", in Lehto, Olli, Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Helsinki: Acad. Sci. Fennica, pp. 557–563, ISBN 978-951-41-0352-0, MR 562655

Jacquet, Hervé (1971), "Représentations des groupes linéaires p-adiques", in Gherardelli, F., Theory of group representations and Fourier analysis (Centro Internaz. Mat. Estivo (C.I.M.E.), II Ciclo, Montecatini Terme, 1970), Rome: Edizioni cremonese, pp. 119–220, doi:10.1007/978-3-642-11012-2, ISBN 978-3-642-11011-5, MR 0291360

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