Filtrations of smooth principal series and Iwasawa modules

Let G be a reductive p-adic groupý. ýWe consider the general questioný ýof whether the reducibility of an induced representation can be detected in aý ý``co-rank oneý" ýsituationý. ýFor smooth complex representations induced from supercuspidalý ýrepresentationsý, ýwe show that a sufficient condition is the existence of a subquotientý ýthat does not appear as a subrepresentationý. ýAn important example is the Langland's quotientý. ýIn additioný, ýwe study the same general question for continuous principal series on p-adic Banach spacesý. ýAlthough we do not give an answer in this caseý, ýwe describeý ýa related filtration on the corresponding Iwasawa modulesý.