\documentclass{amsart}
\usepackage[all, ps]{xy} % Loading the XY-Pic package
                         % Using postscript driver for smoother curves
\usepackage{color}       % For invisible frame
\begin{document}
\thispagestyle{empty} % No page numbers
\SelectTips{eu}{}     % Euler arrowheads (tips)
\setlength{\fboxsep}{0pt} % Frame box margin
{\color{white}\framebox{{\color{black}$$ % Frame for margin

\xymatrix@=6pt{ 
&&\{\pm I\}
  \ar@{^(->}[dd]
\\ \\
   \operatorname{SO}(2k+1)   \ar[dd]^{\wr}  \ar@{^(->}[rr]
 &&\operatorname{O}(2k+1)    \ar@{->>}[dd]  \ar@{->>}[rr]^(.55){\det}
 &&\{\pm 1\}
\\
\\
   \operatorname{PSO}(2k+1)  \ar[rr]^{=}
 &&\operatorname{PO}(2k+1)
}

$$}}} % end math, end frame
\end{document}