Theorem 1.10 [014A] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
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Theorem 1.10
Let f : X → B f:X\rightarrow B T 3 T^{3} b 0 ∈ Δ b_{0}\in\Delta X b 0 X_{b_{0}} G G
(1) X b 0 X_{b_{0}} is of type ( 2 , 2 ) (2,2) and G G is conjugate
to
{ ( 1 0 a 0 1 0 0 0 1 ) | a ∈ 𝐙 } . \left\{\pmatrix{1&0&a\cr 0&1&0\cr 0&0&1\cr}\bigg|a\in{\bf Z}\right\}.
(2) X b 0 X_{b_{0}} is of type ( 2 , 1 ) (2,1) and G G is conjugate
to
{ ( 1 a b 0 1 0 0 0 1 ) | a , b ∈ 𝐙 } . \left\{\pmatrix{1&a&b\cr 0&1&0\cr 0&0&1\cr}\bigg|a,b\in{\bf Z}\right\}.
(3) X b 0 X_{b_{0}} is of type ( 1 , 2 ) (1,2) and G G is conjugate
to
{ ( 1 0 a 0 1 b 0 0 1 ) | a , b ∈ 𝐙 } . \left\{\pmatrix{1&0&a\cr 0&1&b\cr 0&0&1\cr}\bigg|a,b\in{\bf Z}\right\}.
(4) X b 0 X_{b_{0}} is of type ( 1 , 1 ) (1,1) and G G is conjugate
to
{ ( 1 a b 0 1 c 0 0 1 ) | a , b , c ∈ 𝐙 } . \left\{\pmatrix{1&a&b\cr 0&1&c\cr 0&0&1\cr}\bigg|a,b,c\in{\bf Z}\right\}.