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What is the best way to embed a multi-line block of text, surrounded by curly braces, in maths mode? The best I can do is the following hack.

{\text{bounded WD-representations} 
\text{of $W_K$ over $\overline{\mathbf{Q}}_l$}}
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I'm not sure why you think it's hackish, but my guess is because you want it to represent a set, and thus be arbitrarily many lines high? In that case, I would set the text in a \parbox:

\newcommand{\pctext}[2]{\text{\parbox{#1}{\centering #2}}}
\[ \left\{ \pctext{1.8in}{bounded WD-representations of $W_K$ over
                          $\overline{\mathbf{Q}}_l$} \right\} \]

This either allows TeX to break things or to explicitly break text with \\. The downside is that you have to specify the exact width. I tried using the pbox package, which allows you to write \pbox{\textwidth}{...} to get text fitted to the longest line in the ...; unfortunately, I couldn't get \centering to work (except for on the last line), which makes things look really ugly.

Also, in general, the TeX commands which read their previous argument, such as \atop, \atopwithdelims, and thus by extention \brace, aren't recommended. The amsmath package provides the \genfrac command to do this; in your case, you'd have

        {\text{bounded WD-representations}}
        {\text{of $W_K$ over $\overline{\mathbf{Q}}_l$}}

I'm not 100% percent sure why this is, though. But wiser heads than mine have said so, so I tend to pay attention :-)

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