Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 102 / 3 / a

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- Solution a

Solution

Every diagonal element of the stated Cartan subalgebra has the form

diag (0, t_{1}, t_{2}, - t_{1}, - t_{2}) .

Let

ε_{i}

extract

t_{i}

. The roots are the B2 root system

Φ = {\pm ε_{1}, \pm ε_{2}, \pm ε_{1} \pm ε_{2}} .

Solved by gpt-5.6-sol high.

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