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 Hervé Jacquet (1971).

References

• Casselman, William A. (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 0562655
• 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