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I heard a talk recently on number theoretic representation theory, in which the speaker suggested that we focus on the case $G=$GL$_2$, with $\rho$, the representations, being thought of as sym$^n$ for simplicity.

This is all kind of new to me, so I'm rather confused. In this kind of generality and without an ability to furnish more context than I've already given, is it clear what GL$_2$ is? I guess one fixes some kind of a field of coefficients, but I'm not sure.

And more mysterious to me is what exactly the above representation is. Is this standard notation? From what I gather it has something to do with the symmetric power of a representation, but then it seems to me one would have to have an underlying representation first before one can take symmetric powers of it. Or am I on the wrong path completely and is sym$^n$ some kind of a specific representation of GL$_2$?

I hope this is an appropriate question.

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    @Aaron Please consider conver$t$ing your comment into an answer, so that this question gets removed from the [unanswered tab](http://meta.math.stacke$x$change.com/q/3138). If you do so, it is helpful to post it to [this chat room](http://chat.stackexchange.com/rooms/9141) to make people aware of it (and attract some upvotes). For further reading upon the issue of too many unanswered questions, see [here](http://meta.stackexchange.com/q/143113), [here](http://meta.math.stackexchange.com/q/1148) or [here](http://meta.math.stackexchange.com/a/9868).2014-05-27

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