%0 Journal Article
%T Filtrations of smooth principal series and Iwasawa modules
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Alsibiani, W.
%A Ban, D.
%D 2017
%\ 08/30/2017
%V 43
%N Issue 4 (Special Issue)
%P 3-16
%! Filtrations of smooth principal series and Iwasawa modules
%K Parabolically induced representations
%K Iwasawa modules
%K $p$-adic groups
%R
%X 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.
%U http://bims.iranjournals.ir/article_1153_e836ce907c7b77d5c1355c634d744905.pdf