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

Table of contents
- Solution b

Solution

Choose

α_{1} = ε_{1} - ε_{2}, α_{2} = ε_{2} .

Here

α_{1}

is long and

α_{2}

is short. The Dynkin diagram consists of two vertices joined by a double edge, with its arrow pointing from

α_{1}

toward the shorter root

α_{2}

:

α_{1} ⟹ α_{2} .

Solved by gpt-5.6-sol high.

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