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Zbl 0874.22016
Goldberg, David; Herb, Rebecca
Some results on the admissible representations of non-connected reductive $p$-adic groups. (English)
[J] Ann. Sci. Éc. Norm. Supér. (4) 30, No. 1, 97-146 (1997). ISSN 0012-9593

Let $G$ be a $p$-adic reductive group and let $G^0$ be its (Zariski-) connected component. Assume that the component group $G/G^0$ is abelian. The paper under review is concerned with the extension of results known for connected groups to the present case. The authors describe the structure of the induced representation $\text {Ind}^G_{P^0} (\sigma)$, $P^0$ a parabolic of $G^0$ and $\sigma$ a discrete series representation of the Levi component of $P^0$. They develop an appropriate theory of $R$-groups which rule the decomposition of the induced representation. Intertwining operators are examined and notions of supercuspidal and discrete series representations are given.
[A.Deitmar (Heidelberg)]

MSC 2000:: *22E50 Repres. of Lie and linear algebraic groups over local fields
22E35 Analysis on p-adic Lie groups

Keywords: $p$-adic reductive group; $R$-groups; intertwining operators; induced representation

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