A group of automorphisms of the rooted dyadic tree and associated Gelfand pairs (Q2389056)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A group of automorphisms of the rooted dyadic tree and associated Gelfand pairs |
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A group of automorphisms of the rooted dyadic tree and associated Gelfand pairs (English)
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22 July 2009
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Summary: We study the group \(G\) of automorphisrns of the rooted dyadic tree generated by translation by 1 and multiplication by an odd integer \(q\), showing that \(G\) admits a self-similar presentation and it is isomorphic to the Baumslag-Solitar group \(BS_q\). Moreover, we show that the action of \(G\) on each level of the tree gives rise to a Gelfand pair.
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