documentclass{amsart}
usepackage{dynkin-diagrams}
begin{document}
Page 56:
pgfkeys{/Dynkin diagram,arrows=false}
[
begin{array}{cc}
A_1 times A_1 & dynkin{A}{1}dynkin{A}{1}\
A_2                     & dynkin{A}{2}\
B_2                     & dynkin{B}{2}\
G_2                     & dynkin{G}{2}
end{array}
]

Page 57:
pgfkeys{/Dynkin diagram,arrows=true}
[
begin{array}{cc}
B_2                     & dynkin{B}{2}\
G_2                     & dynkin{G}{2}
end{array}
]
end{document}