Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 302 / 4 / d

Table of contents
- Solution d

Solution

This is the G2 root system, with

α

long and

β

short. Its positive roots are

β, α, α + β, α + 2 β, α + 3 β, 2 α + 3 β,

and the full root set includes their negatives. Thus

dim g = 12 + 2 = 14

. Finally

4 cos^{2} θ = A_{12} A_{21} = 3,

and simple roots have obtuse angle, so

θ = 5 π /6

.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version