On tempered representations of a reductive non-connected \(p\)-adic group: the case that \(G/G^0\) is commutative and finite. (Sur les représentations tempérées d’un groupe réductif \(p\)-adique non connexe: Cas où \(G/G^0\) est commutatif et fini.) (French) Zbl 1463.11112

Bettaïeb, Karem

Math. Bohem. 142, No. 4, 387-403 (2017).

Recall the Summary of K. Bettaïeb [Algebr. Represent. Theory 16, No. 1, 275–287 (2013; Zbl 1395.20031)]: Let \(G\) be the group of points defined over a \(p\)-adic field of a non-connected reductive group. In this note, we prove that every tempered irreducible representation of \(G\) is irreducibly induced from an essential one of a cuspidal Levi subgroup of \(G\).
The author now revisits this situation in the case that \(G/G^0\) is commutative and finite, where \(G^0\) denotes the identity component of \(G\).

Reviewer: Wilberd van der Kallen (Utrecht)

MSC:

11E95	\(p\)-adic theory
20G05	Representation theory for linear algebraic groups
20G15	Linear algebraic groups over arbitrary fields

Keywords:

reductive \(p\)-adic group; tempered representation

Citations:

Zbl 1395.20031