Lowercase \mathcal

I'm a bit surprised that Will Robertson hasn't dropped by and mentioned the STIX fonts as these have the lowercase calligraphic (and lowercase blackboard bold) glyphs.

There doesn't yet seem to be a simple LaTeX package available mapping all the glyphs to particular commands, though. The stix package on CTAN at present seems to be just a copy of the fonts themselves (reorganised into correct texmf tree layout) but no style files as yet. I recall reading on the STIX website that LaTeX-related stuff was intended, but given how long it took the fonts to be released, I'm not holding my breath!

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As of 2018, this is now quite easy using luatex or xetex:

\documentclass{article}
%\url{https://tex.stackexchange.com/q/479/86}
\usepackage{amsmath}
\usepackage{fontspec}
\usepackage{unicode-math}
\setmainfont{TeX Gyre Pagella}

% Any of the following work, and probably many more
%\setmathfont{TeX Gyre Pagella Math}
%\setmathfont{TeX Gyre Termes Math}
%\setmathfont{STIX}
\setmathfont{Asana Math}

\begin{document}
\begin{gather*}
{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \\
{abcdefghijklmnopqrstuvwxyz} \\
\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \\
\mathcal{abcdefghijklmnopqrstuvwxyz} \\
\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \\
\mathscr{abcdefghijklmnopqrstuvwxyz} \\
\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \\
\mathbb{abcdefghijklmnopqrstuvwxyz} \\
\end{gather*}
\end{document}

As pointed out in the comments, you need to use \mathscr (or \let\mathcal=\mathscr).

A lowercase L can be done with \ell. But this seems to be the only lowercase letter that is included without loading any packages.

The font package boondoxo has both lowercase and uppercase calligraphic math symbols, as well as their bold versions. You may load it by \usepackage[cal=boondoxo]{mathalfa}, and see whether you like it.