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What is the best way to translate the mathematical term ''intertwiner'' (between two representations of a group) into German?

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6  
Pretty related. –  NikolajK Jul 18 '12 at 14:03
    
Which horrible university forces you to give lectures in German ;) Anyway, naively I would try to take any translation of entwine and incorporate inter –  Simon Markett Jul 18 '12 at 14:06
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Taking J.S. Milne's 11th tip one step further? :-) –  Asaf Karagila Jul 18 '12 at 14:08
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@SimonMarkett: I'd guess an university in Germany (or another country where German is the native language). You generally expect lectures to be given in the native language, don't you? –  celtschk Jul 18 '12 at 14:18
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@AsafKaragila: I have people complaining about german being hard to learn and listen to at least 3 times a week, so it's not really funny. (Unless you're Mark Twain.) –  NikolajK Jul 18 '12 at 14:41
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3 Answers

Excuse me if mine is a very low-brow approach.

Let us look at the English Wikipedia page Equivariant Maps (cf. here), where there is the definition of Interwiners, as a special kind of equivariant maps.
Then let us switch to the German version, and we find that, in the same context, it is employed just the term äquivarianten Abbildung.

I hope it helps. Bye.

Edit Added because the OP need not only tranlations but references to actual usage.
In the German literature you'll find it also in the abbreviated form $G$-Abbildung as for example here in Tammo Von Dieck's Topologie,
(In order to overcome the difficulties you report in comments, here is the exact physical reference: Chapter I, Section 10, second paragraph on page 41.)

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I had done just that before posting the question, but I would have liked to have a single word translation rather than 9 syllables. - Would the term ''äquivariante Abbildung'' also be appropriate for intertwiners between representations of an algebra? –  Arnold Neumaier Jul 18 '12 at 14:09
    
@ArnoldNeumaier I have added a reference using just G-Abbildung. –  Giuseppe Tortorella Jul 20 '12 at 17:16
    
google books says that it is not avialable to me for viewing. Could you please give the page number? –  Arnold Neumaier Jul 21 '12 at 20:07
    
From Google Books (to me the page was displayed): 40 41 42 –  Martin Sleziak Jul 25 '12 at 14:03
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My old Technik-Wörterbuch (1982) directs me from intertwine to interlace, which it translates by verschlingen (Verschlingung, verschlungener Zyklus), which I think sounds right. These words are marked as topological terms, though, so you will have to consider if they are suitable in an algebraic context.

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It is not enough to find possible translations; since the concept is old one also needs references for actual usage in this context. (Verschlingung sounds more like braiding, which has a very different meaning in group theory.) –  Arnold Neumaier Jul 18 '12 at 16:40
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The link http://mathoverflow.net/questions/46061/what-is-the-german-translation-for-intertwiner provided by Nick Kidman was quite useful. I found two old German papers by authorities in group theory
- Brauer: http://www.springerlink.com/content/g7465w3g08255142/
- Tamaschke: http://www.springerlink.com/content/t85t8k7731088573/
who use ''verkettet'' for the relationship, which suggests the name Verketter, which can indeed be found in recent lecture notes by
- Rehren: http://www.theorie.physik.uni-goettingen.de/~rehren/ps/cqft.pdf
although Rehren subsequently uses the word Intertwiner as a German Lehnswort for this concept.

Edit: p.273 of arXiv:hep-th/9805093v1 explicitly says '' intertwiners (“Verketter” in the sense of Schur)'', and Schur was probably the first one to use the concept at all. Indeed, in his paper ''Beiträge zur Theorie der Gruppen linearer homogener Substitutionen'' Trans. Amer. Math. Soc. 10 (1909), 159--175. http://www.jstor.org/stable/10.2307/1988680 , Schur uses in this context the adjective ''verkettet'', but not the substantive.

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