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I'd like to create some custom symbols for double affine Hecke algebras. Specifically, I would like to "double" the usual "H" symbols, for example $\mathcal{H}$, $\mathbb{H}$ or $\mathbf{H}$. By doubling I mean putting two H symbols together so that we obtain an "H" with three verticals bars. Does anyone know how to do it? Thanks a lot!

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    \( \mathcal{H}\mkern-6mu\mathcal{H} \) is a start, but the end strokes on the standard calligraphic fonts are wide enough to overlap with the other vertical strokes of the H once you get the letters close enough for the central vertical strokes to overlap. – Mike Renfro May 12 '16 at 13:20
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    \newcommand{\Hecke}{\textbf{H\kern-.38em H}} works pretty well, and since the backspace is in terms of the current em width, it should work in just about any size or environment. (this is the simplest to construct, since all strokes are symmetrical. may not be the same for fonts other than computer modern.) – barbara beeton May 12 '16 at 13:29
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It may or may not be to your taste...for example, the slanted + is not the same slant as the \mathcal{H} legs; but it works in all math styles.

\documentclass{article}
\usepackage{graphicx,trimclip,scalerel}
\def\dblHtextstyle{\clipbox{0pt 0pt 4pt 0pt}{$\mathcal{H}$}\smash{
  \kern-1pt\scalebox{.75}[1.06]{\raisebox{.450pt}{\textsl{\sffamily +}}}\kern-5.15pt
  \kern-1pt\scalebox{.75}[1.04]{\raisebox{.463pt}{\textsl{\sffamily +}}}\kern-5.15pt
  \kern-1pt\scalebox{.75}[1.02]{\raisebox{.476pt}{\textsl{\sffamily +}}}\kern-5.15pt
  \kern-1pt\scalebox{.75}[1.00]{\raisebox{.489pt}{\textsl{\sffamily +}}}\kern-1pt
  \clipbox{4pt -2pt 0pt 0pt}{$\mathcal{H}$}}}
\def\dblH{\scalerel*{\dblHtextstyle}{\mathcal{H}}}
\begin{document}
$\mathcal{H}\dblH_{\dblH_{\dblH}}$
\end{document}

enter image description here

For a version with a better slant, but which only works in pdflatex, here is an alternative, using Bruno's \slantbox (Shear transform a "box"):

\documentclass{article}
\usepackage{graphicx,trimclip,scalerel}
\newsavebox{\foobox}
\newcommand{\slantbox}[2][.5]
  {%
    \mbox
      {%
        \sbox{\foobox}{#2}%
        \hskip\wd\foobox
        \pdfsave
        \pdfsetmatrix{1 0 #1 1}%
        \llap{\usebox{\foobox}}%
        \pdfrestore
      }%
  }
\def\dblHtextstyle{\clipbox{0pt 0pt 4pt 0pt}{$\mathcal{H}$}\smash{\slantbox[.25]{
  \kern-5.2pt\scalebox{.75}[1.06]{\raisebox{.450pt}{\sffamily +}}\kern-4.97pt
  \kern-1pt\scalebox{.75}[1.04]{\raisebox{.463pt}{\sffamily +}}\kern-4.97pt
  \kern-1pt\scalebox{.75}[1.02]{\raisebox{.476pt}{\sffamily +}}\kern-4.97pt
  \kern-1pt\scalebox{.75}[1.00]{\raisebox{.489pt}{\sffamily +}}\kern-1pt}
  \clipbox{4pt -2pt 0pt 0pt}{$\mathcal{H}$}}}
\def\dblH{\scalerel*{\dblHtextstyle}{\mathcal{H}}}
\begin{document}
$\mathcal{H}\dblH_{\dblH_{\dblH}}$
\end{document}

enter image description here

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