Relative subrepresentation theorem for a finite central extension of a reductive group

Chengyu Jiao, William Banks

Abstract: Jacquet's subrepresentation theorem asserts that any irreducible admissible representation of a reductive p-adic group is a subrepresentation of $Ind^G_P ([\tau])$, where P is a parabolic subgroup of G and [\tau] is a cuspidal representation. Kato and Takano extended this theorem to the H-relatively cuspidal case. In this dissertation, we work on the level of finite central extensions, and extend Kato and Takano's results to the finite central extension case.