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.
Alsibiani, W., & Ban, D. (2017). Filtrations of smooth principal series and Iwasawa modules. Bulletin of the Iranian Mathematical Society, 43(Issue 4 (Special Issue)), 3-16.
MLA
Alsibiani, W., & Ban, D. "Filtrations of smooth principal series and Iwasawa modules", Bulletin of the Iranian Mathematical Society, 43, Issue 4 (Special Issue), 2017, 3-16.
HARVARD
Alsibiani W., Ban D. (2017). 'Filtrations of smooth principal series and Iwasawa modules', Bulletin of the Iranian Mathematical Society, 43(Issue 4 (Special Issue)), pp. 3-16.
CHICAGO
W. Alsibiani & D. Ban, "Filtrations of smooth principal series and Iwasawa modules," Bulletin of the Iranian Mathematical Society, 43 Issue 4 (Special Issue) (2017): 3-16,
VANCOUVER
Alsibiani W., Ban D. Filtrations of smooth principal series and Iwasawa modules. BIMS. 2017;43(Issue 4 (Special Issue)):3-16.
