Filtrations of smooth principal series and Iwasawa modules

Let G be a reductive p-adic group. We consider the general question of whether the reducibility of an induced representation can be detected in a ``co-rank one" situation. For smooth complex representations induced from supercuspidal representations, we show that a sufficient condition is the existence of a subquotient that does not appear as a subrepresentation. An important example is the Langlands' quotient. In addition, we study the same general question for continuous principal series on p-adic Banach spaces. Although we do not give an answer in this case, we describe a related filtration on the corresponding Iwasawa modules.