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

Table of contents
- Solution iv

Solution

ε_{1} \mapsto ε_{1}, ε_{2} \mapsto ε_{2}, ε_{3} \mapsto - ε_{3}

preserves

Φ

and exchanges

α_{2}

with

α_{3}

while fixing

α_{1}

. It is not in the

D_{3}

Weyl group, whose signed permutations change an even number of signs. Thus it is an outer automorphism of the root system.

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