Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43Issue 4 (Special Issue)20170830Filtrations of smooth principal series and Iwasawa modules3161153ENW.AlsibianiD.BanJournal Article20170513Let $G$ 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.<br /> http://bims.iranjournals.ir/article_1153_e836ce907c7b77d5c1355c634d744905.pdf