Abstract: We will see some consequences of Harish Chandra's theorem, including Jacquet's subrepresntation theorem which asserts that any irreducible smooth representation of a reductive p-adic group G is a subrepresentation of Ind_P^G(\sigma), where P=MN is a parabolic subgroup of G and \sigma is an irreducible representation of M. In the latter part, we will look into examples of irreducible supercuspidal representation of GL(F,2).
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