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I'm trying to get an idea of Drinfeld's Zastava space. It seems to be an infinite-dimensional version of the flag variety, for affine Lie algebras.

But, first of all, why is it called Zastava (Застава)? Sadly I don't understand Russian and I don't understand the connotation. Googling gave me this Wikipedia article about a car company first. But I don't think a car company has much to do with these spaces, or does it?

Apparently it means "outpost" in Russian. But why an outpost? Drinfeld seems to be Ukrainian (again, from Wikipedia) and zastava means "pledge"?

Is it an outpost to a greater understanding of these spaces? Is it a pledge of mathematicians to understand more???

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+1 for trying all the obvious things first! –  José Figueroa-O'Farrill Dec 30 '10 at 10:09
I've never heard about the Ukranian meaning "pledge" for "zastava" (which is, BTW, an old word in Slavic). My dictionary returns "1) (histor.) gate, turnpike; 2) (military) outpost; picket, security detachment." To my taste, "turnpike" is better than "outpost" and you may count flags as pikes. –  Wadim Zudilin Dec 30 '10 at 13:47
The word "zastava" means "flag" in Croatian (or Serbian). I. Mirkovic is Croatian, so maybe that's the explanation. –  Antun Milas Dec 30 '10 at 13:53
Antun, that's indeed a nice etymologic reason. I would suggest you putting your comment as answer. –  Wadim Zudilin Dec 30 '10 at 14:03
@Wadim: all my Slavic is based on translate.google.com ... Please blame google:p What did zastava mean in proto-Slavic, say in the church Slavonic? @Antun; thanks! I'll accept your answer once you post it below. So it just meant the flag space ... –  Yuji Tachikawa Dec 30 '10 at 14:12

2 Answers 2

up vote 25 down vote accepted

The term was coined by one Michael de Finkelberg during his visit to Croatia. The word is indeed Croatian and means ``flag''. I was happy to have a Croatian word in mathematics. The strategy of giving a new notion an old name but in a different language is not perfect.

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I've certainly heard of worse naming strategies.... –  Ben Webster Jan 10 '11 at 1:40
Now, how do you translate "flag variety" in Croatian? –  Laurent Moret-Bailly Jan 10 '11 at 7:58

The word "zastava" means "flag" in Croatian (or Serbian). I. Mirkovic, one of the authors of the paper linked by Yuji, is Croatian, so maybe that's the explanation.

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I've heard that zaszlo is "flag" in Hungarian, but didn't think it had any relation to my name (probably originally Zaslowski and Ukrainian) -- Uralic vs. Slavic. In any case I will now try harder to understand flag varieties. –  Eric Zaslow Jan 10 '11 at 1:52
Whatever the case, the Hungarian word "zaszlo" is of Slavic origin. –  Péter Komjáth Oct 19 '11 at 17:50

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