 D3 root system

ID: d3-root-system

The

D_{3}

roots are

\pm ε_{i} \pm ε_{j}

for

1 \leq i < j \leq 3

α_{1} = ε_{1} - ε_{2}, α_{2} = ε_{2} - ε_{3}, α_{3} = ε_{2} + ε_{3}

form the three-node chain

α_{2} - α_{1} - α_{3}

, so

D_{3} ≅ A_{3}

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