\documentstyle[12pt]{article}
\topmargin .15in
\oddsidemargin 0in
\parindent 0in
\parskip .1in
\textheight 8.3in
\textwidth 6.2in
\setlength{\unitlength}{1.2cm}
\begin{document}

{\large We have the (P-local) commutative diagram:}

\begin{picture}(7,12)

\put(11,6){$Sp(n+1)$}
\put(11,4){$SU(2n+2)$}
\put(11,2){${SU(2n+2)}\over{Sp(n+1)}$}
\put(6,4.5){$Sp(l+1)$}
\put(3,4){$\Sigma^4SO(2n+1)$}
\put(0,2.5){$\Sigma^4SO(2l+1)$}
\put(6,2.5){$SU(2l+2)$}
\put(6,.3){${SU(2l+2)}\over{Sp(l+1)}$}
\put(7.9,4.7){\vector(3,1){3.1}}
\put(8,2.7){\vector(3,1){3.1}}
\put(7.6,0.5){\vector(3,1){3.3}}
\put(1.8,2.9){\vector(3,1){2.1}}
\put(11.6,5.8){\vector(0,-1){1.4}}
\put(11.6,3.9){\vector(0,-1){1.3}}
\put(2.6,2.6){\vector(1,0){2.8}}
\put(5.7,4.1){\line(1,0){.7}}
\put(6.7,4.1){\vector(1,0){4.2}}
\put(6.6,4.3){\vector(0,-1){1.5}}
\put(6.6,2.4){\vector(0,-1){1.4}}
\put(.5,3){\line(0,1){1.605}}
\put(.5,4.605){\vector(1,0){4.95}}
\put(3.5,4.5){\line(0,1){.05}}
\put(3.5,4.7){\line(0,1){1.4}}
\put(3.5,6.1){\vector(1,0){7.4}}

\end{picture}
\end{document}