Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 102 / 3 / b / i

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- Solution i

Solution

The diagonal Cartan subalgebra consists of

diag (t_{1}, t_{2}, t_{3}, - t_{1}, - t_{2}, - t_{3}) .

Let

ε_{i} \in t^{*}

read off

t_{i}

. The roots are

Φ = {\pm ε_{i} \pm ε_{j} : 1 \leq i < j \leq 3},

the D3 root system.

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