Using user defined commands within Tikzcd

Question

\documentclass{article}
\usepackage{amsmath,amscd,amssymb,amsthm,graphicx,amsxtra}
\usepackage{verbatim}
\usepackage{tikz-cd,xparse}
\usetikzlibrary{matrix,arrows,decorations.pathmorphing}
\newcommand {\dc}[3]{$#1_{#2,#3}$}
\begin{document}
\begin{tikzcd}
 {} \dc B {-2} 2 \arrow[dotted]{l}  &\dc B {-1} 2 \arrow{l}  &dc B 0 2 \arrow{l}  &\dc B 1 2 \arrow{l}  & \dc B 2 2 \arrow{l} &{} \arrow[dotted]{l}\\
\end{tikzcd}
\end{document}

I wrote this and several variants of it (using braces, with no space, with 'ampersand replacement' and so on) to produce and sadly none of it worked. I know I can get around it by using (_) but would like to know why my code wasn't working. I need to produce several of such images and objects, this (for me) was the first step towards defining a newcommand but it failed miserably. The error which keep appearing is

Package pgfbasematrix Error: Single ampersand used with wrong catcode.

Answer 1

Cells in a tikzcd environment are expected to be in math mode, so your definition of \dc should omit the $ signs.

\documentclass{article}
\usepackage{amsmath,amssymb,amsthm,graphicx}
\usepackage{tikz-cd}
\usetikzlibrary{matrix,arrows,decorations.pathmorphing}

\newcommand {\dc}[3]{#1_{#2,#3}}

\begin{document}

\begin{tikzcd}
  {} &
  \dc{B}{-2}{2} \arrow[dotted]{l} &
  \dc{B}{-1}{2} \arrow{l} &
  \dc{B}{0}{2} \arrow{l} &
  \dc{B}{1}{2} \arrow{l} &
  \dc{B}{2}{2} \arrow{l} &
  {} \arrow[dotted]{l}
\end{tikzcd}

\end{document}

I prefer always using braces around arguments, although it's not strictly required by the syntax. In this case, however, I don't see any real advantage over typing

B_{-2,2}

Answer 2

If I understand your comment below egreg's answer correctly, you want to have the possibility to write your command outside of math environments as well. egreg already explained what is happening with your MWE. If you just add an \ensuremath to his solution, you will be able to use this command where ever you like.

% arara: pdflatex

\documentclass{article}
\usepackage{tikz-cd}
\newcommand{\dc}[3]{\ensuremath{#1_{#2,#3}}}

\begin{document}
In text it would look like \dc{B}{1}{2}. In inline math it looks the same with $\dc{B}{1}{2}$. Display math looks like this:
\[\dc{B}{2}{3}\]    
Finally, you can use it in your commutative diagrams:

\begin{tikzcd}
    \null 
    & \dc{B}{-2}{2} \arrow[dotted]{l} 
    & \dc{B}{-1}{2} \lar 
    & \dc{B}{0}{2} \lar 
    & \dc{B}{1}{2} \lar 
    & \dc{B}{2}{2} \lar 
    & \null \arrow[dotted]{l}
\end{tikzcd}
\end{document}