The reason I came by Ben’s notes on translations from the German was because I received an email from Jean-François in France, or at least via wanadoo.fr, on the topic of resp., which he said is OK in mathematics contexts. He had read on my blog that the abbreviation resp. doesn’t exist in English.
It is used in mathematics.
For an example, go to:
And search for “resp.” in the page.
Or do a Google search with: resp. mathematics.
I have to admit that this page and numerous other Ghits (© Trevor) cast serious doubt on my opinion. However, I do note that the author of this page is called Gérard P. Michon. He did his Ph.D. in Los Angeles, but there’s something not quite American about his name. And so it is with other Ghits (I haven’t looked at all of them).
So I wrote to Ben, who translates maths, but he didn’t seem too keen on resp. either.
Jean-François had been asked by an American technical writer from his company what he meant by resp. He also added – ‘just for fun’ – the following, which I pass on as I haven’t been able to digest it:
On supports of induced representations for symplectic and odd-orthogonal groups.
Let G be Sp(2n,F) (resp. SO(2n+1,F)), where F is a p-adic field of characteristic zero. In this paper, we give a correspondence which associates to an irreducible representation π of G an m-tuple of irreducible representations of lower rank symplectic (resp. orthogonal) groups based on the supercuspidal support of π. We show that this correspondence respects the induction and Jacquet module functors (in a sense to be made precise), as well as verifying a number of other useful properties. In essence, this correspondence allows one to isolate the effects of the different families of supercuspidal representations of general linear groups which appear in the support of π.
Meanwhile, someone else came to my site looking for resp. The search also threw up a discussion between some people in the USA on the use of respectively. One of them had written ‘Respectfully submitted by …’ and had this corrected to ‘Respectively submitted by …’ It was posited, of course, that this might be British usage. Finally the questioner decided to omit the word altogether.