# On 'backslash-forward slash' notation

I am curious about a notation that I have seen, but I have only seen it in contexts beyond my current level of ability and so haven't learned its meaning. Also, it's often difficult to search for the meaning of notations. It appears to be group theoretic in nature.

The notation uses a backslash followed by a forward slash, like so: $\text{SL}_n\mathbb{Z} \setminus \text{SL}_n\mathbb{R} \,/ \,\text{SO}(n)$.

Of course it may be a 'set minus' followed by a 'modded by', but I'm not so sure. So what's the meaning of this notation, and in what contexts is it most often used? Thanks.

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Here ya go. It's a double coset space.

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Cool, thanks! Where would one first encounter this? Just in an advanced group theory text, or in a more specific subfield? –  Alex Petzke Nov 4 '12 at 2:56
Most advanced group theory texts will have double cosets - I first saw them in Hall's. Usually you'll see the space of them referred to in representation theory or something specifically about lie groups. –  Alexander Gruber Nov 4 '12 at 3:09
Got it, thanks. –  Alex Petzke Nov 4 '12 at 4:02