On reducibility of \(p\)-adic principal series representations of \(p\)-adic groups (Q2827393)
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scientific article; zbMATH DE number 6640992
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On reducibility of \(p\)-adic principal series representations of \(p\)-adic groups |
scientific article; zbMATH DE number 6640992 |
Statements
19 October 2016
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\(p\)-adic representations
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\(p\)-adic groups
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principal series
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On reducibility of \(p\)-adic principal series representations of \(p\)-adic groups (English)
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The class of \(p\)-adic principal series representations, an important class of \(p\)-adic representations of reductive \(p\)-adic groups, was introduced in the general setting by \textit{P. Schneider} and \textit{J. Teitelbaum} [Isr. J. Math. 127, 359--380 (2002; Zbl 1006.46053)]. The authors show that such representations are irreducible when the inducing character lies in a certain cone. This is consistent with a conjecture of Schneider regarding the semisimple case [\textit{P. Schneider}, in: Proceedings of the international congress of mathematicians (ICM). Volume II: Invited lectures. Zürich: European Mathematical Society (EMS). 1261--1282 (2006; Zbl 1138.22014)].
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