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