I came across the following notation in this document
$_{GL(k)}\backslash \text{Mat}^*(k,n)$
What does $_A\backslash B$ mean, where $A$ and $B$ are suitable mathematical objects?
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$\begingroup$ What's the context? It looks like this could be a strange way to denote a quotient. That would make sense based on what you've given, if that has no other accepted meaning. $\endgroup$– florenceJul 6, 2016 at 18:59
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$\begingroup$ @florence- The context is given on Pg. 3 $\endgroup$– user67803Jul 6, 2016 at 19:02
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$\begingroup$ @florence It's pretty much the first line or two after the table of contents, when they define grassmanians. It looks like they're quotienting matrices by row operations $\endgroup$– snultyJul 6, 2016 at 19:02
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1 Answer
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When a group $G$ has a right-action on a set $E$, $G\backslash E$ denotes the set of orbits of this action.
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1$\begingroup$ The point of this notation is that sometimes you want to quotient by both some group acting on the left, and some other group acting on the right. These get you double cosets: en.wikipedia.org/wiki/Double_coset $\endgroup$ Jul 6, 2016 at 19:21