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I'm searching for a translation for the term "intertwiner" in German.

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    $\begingroup$ Have you tried looking at some papers by German representation theorists who use the technique? $\endgroup$ Nov 14, 2010 at 19:08
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    $\begingroup$ It is amusing to recall once seeing some book in English published in maybe about 1950 whose author explained that there's no English word corresponding to the German word Faltung, so that was what he used. Apparently convolution became standard more recently than that. $\endgroup$ Nov 15, 2010 at 16:42
  • $\begingroup$ A related post on Mathematics: Intertwiner in german? (From 2012 - later than this question.) $\endgroup$ May 30, 2022 at 9:14

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I (native speaker) learned the term "Vertauschungsoperator" in my undergraduate courses. Unfortunately I cannot cite any reference right now, except the fact that the lecturer of the courses, Prof H.S. Holdgruen, is very sensible in his use of the german language. Therefore I estimate the probability very high that this is a common term in german texts on representation theory.

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  • $\begingroup$ I can confirm that this is standard terminology in the German representation theory community (at least as far as I can tell from the members I know). The only reference I know by heart, however, is the German PhD thesis of Martin Olbrich. $\endgroup$
    – B K
    May 30, 2022 at 19:34
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I think it can be translated as Verketter or Vermittler. See e.g. Karl-Henning Rehren's Konforme Quantenfeldtheorie on p.128. But I should warn that I am not a native speaker.

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    $\begingroup$ Personally (and I am a a native speaker) I have never heard about Verketter or Vermittler. I would just say G-äquivariante Abbildung. $\endgroup$ Nov 14, 2010 at 19:27
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    $\begingroup$ Ah ok, thanks, I was already surprised that a google search for these words didn't give many results. $\endgroup$ Nov 14, 2010 at 19:29
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    $\begingroup$ Anyway, in the PDF I'm referring to, it denotes a linear operator $V$ such that $V \rho(A) = \sigma(A) V$ for two representations of an algebra $A$, so the setting is slightly different. $\endgroup$ Nov 14, 2010 at 19:32
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    $\begingroup$ @Pieter: On the numbered page 126 in the PDF, one finds "als Intertwiner bezeichnet (Verketter, Vermittler)". To me it seems easiest just to use "Intertwiner" even if it's not quite an echt German word. In mathematics, technical terms seem to migrate frequently across linguistic lines not covered by dictionaries. $\endgroup$ Nov 15, 2010 at 11:30
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    $\begingroup$ Pieter: What's the difference to "$G$-equivariant"? Or "$G$-homomorphism"? $\endgroup$ Nov 15, 2010 at 16:20

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