The unnormalized Jacquet module is the space of coinvariants of a unipotent subgroup . If a subgroup normalizes , it acts on this quotient. Every linear functional transforming by a linear character trivial on factors through it. Normalized Jacquet functors include an additional modulus twist; that convention must be specified.
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The Jacquet module is a concept from representation theory and has its roots in the theory of automorphic forms. It is primarily associated with the study of representations of reductive groups over local or global fields, particularly in the context of Maass forms, automorphic representations, and the theory of the Langlands program.