Subtile finesse de la notation…

For a long time (since I first heard of it around 1990), I thought that the terminology “Property (T)” was a completely arbitrary name, and no better than the thousand notions of “admissible thingummy” or “good khraboute” which sprinkle too many mathematics papers. Then I learnt a few years ago that the “T” was supposed to refer to the Ttrivial representation, since — in a suitable language — the property is about the trivial representation of a group G.

This was already better. But much more recently, I learnt from S. Mozes that the typography “(T)” itself was not some random choice, but was meant to express the fact that the trivial representation T is supposed to be alone in some open set, incarnated as an open interval (so one should read () as in (a,b))…

A direct corollary is that the right translation in French is, of course, Property ]T[.

By the way, I personally much prefer the ]a,b[, [a,b], ]a,b], etc, notation for intervals, but I’m told that many find this ugly beyond belief and much prefer the (a,b), (a,b], etc, style…

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Kowalski

I am a professor of mathematics at ETH Zürich since 2008.

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