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I search a translation for the term "intertwiner" into german.

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Have you tried looking at some papers by German representation theorists who use the technique? – Adam Hughes Nov 14 '10 at 19:08
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. – Michael Hardy Nov 15 '10 at 16:42
up vote 6 down vote accepted

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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I think it can be translated as Verketter or Vermittler. See e.g on p.128. But I should warn that I am not a native speaker.

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Personally (and I am a a native speaker) I have never heard about Verketter or Vermittler. I would just say G-äquivariante Abbildung. – Andreas Thom Nov 14 '10 at 19:27
Ah ok, thanks, I was already surprised that a google search for these words didn't give many results. – Pieter Naaijkens Nov 14 '10 at 19:29
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. – Pieter Naaijkens Nov 14 '10 at 19:32
@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. – Jim Humphreys Nov 15 '10 at 11:30
Pieter: What's the difference to "$G$-equivariant"? Or "$G$-homomorphism"? – darij grinberg Nov 15 '10 at 16:20

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