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Non-Archimedean induced representations of compact zerodimensional groups. (English) Zbl 0585.22007

Let \(p\) be an odd prime number, let \(K\) be an algebraically closed non- Archimedean valued complete field. One assumes that the characteristic of the residue class field of \(K\) is not \(p\). By using techniques of induced representations the author describes all irreducible unitary representations of certain (compact) matrix groups \(G\) over \(\mathbb{Q}_ p\) (for example, \[ G = \left\{ \begin{pmatrix} \alpha & \varepsilon & \varphi \\ 0 & \beta & \delta \\ 0 & 0 & \gamma \end{pmatrix} \;:\;\alpha,\beta,\gamma \in 1+p\mathbb{Z}_ p; \quad\delta,\varepsilon,\varphi \in p\mathbb{Z}_ p\right\}) \] into non-Archimedean Banach spaces over \(K\).
Reviewer: W.Schikhof

MSC:

22C05 Compact groups
22D10 Unitary representations of locally compact groups
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
20G25 Linear algebraic groups over local fields and their integers
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References:

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