\documentclass[12pt]{article}

\usepackage{makeidx}
\makeindex

\usepackage[quickindex]{xepersian}
% if you want use quickindex to index automatically, you must run this:
%xelatex --shell-escape -interaction=nonstopmode -synctex=-1 %.tex
\settextfont{Yas}
\begin{document}

\lr{abc}%
\index{\lr{abc}}

$\alpha$%
\index{alpha@$\alpha$}

$\beta$%
\index{beta@$\beta$}

%$\|  \cdot \|$%
%\index{mter normal@$\left \vert   \cdot \right \vert $}

$\left \Vert   \cdot \right \Vert $%
\index{mter normal2@$\left \Vert   \cdot \right \Vert $}

$C_{K!}$
\index{$C_{K"!}$}


%\index{$\mu^{\otimes\downarrow n}$}
%\index{$\mu^{\otimes\protect\downarrow n}$}
%\mbox{\index{$\mu^{\otimes\protect\downarrow n}$}}
%\mbox{\index{$\|  \cdot \|$}}


\printindex
\end{document}
% type in mymaths.xdy:
% (merge-rule "\alpha" "alpha" :string)
%
%xindy -M mymaths.xdy -L persian -C utf8 -M texindy -M page-ranges filename.idx