Notation for subgroup of $\mathrm{GL}(n)$ consisting of matrices with determinant +1 or -1? $\mathrm{SL}(n)$ is the standard notation for the subgroup of matrices with determinant $1$, but what about the subgroup of all matrices with determinant $+1$ or $-1$? Is there a standard notation for this in the literature? 
I am considering using $\mathrm{SL}_{\pm}(n)$ to denote this group, but if there is already a standard notation in the literature I would prefer to use that instead.
 A: As a group theorist I can't recall seeing such a notation and so I would suggest that it is sufficiently uncommon that you can use your own notation without offense.  I might suggest it be a superscript since many conventions that include the field will place the dimension or the field in the subscript position, e.g. $SL^{\pm}_n(K)$ and $SL^{\pm}_K(n)$ would both fit with common patterns.
That said, I wouldn't invest much in promoting the notation as it seems it would open pointless debate. The notation schemes that seem to be here to stay revolve around a connection to a geometric condition, a Lie condition, or are necessary to give names to associated simple groups.  So while $\det(x)=\pm 1$ is natural and motivate $SL^{\pm}(n)$, someone might argue it natural to include other roots of unity or whatever subgroup $U$ of scalars.  But something like $SL^U(n)$ is starting to get silly.  Some group theorist like notation like $2.SL(n)$ to indicate a degree 2 extension (a double cover) but that leaves it as ambiguous "which" extension is implied.  Still, a common notation you would find in print.  You could also write $\mathbb{Z}_2\ltimes SL(n)$ but that starts to get verbose and suffers the same ambiguity as $2.SL(n)$.
