Anybody here who could explain to me in the simplest terms what is so

  • Thread starter Lapidus
  • Start date
  • #1
343
11
Anybody here who could explain to me in the simplest terms what is so special about the Lie group SO(8) and what is meant by triality?

I know some Lie and representation theory, mostly from physics books. As I understand there are vector and spinor representations for so(n). If n is even, there are two spin reps and one vec rep, if n is odd there is one spin rep and one vec rep.

For example, for n=4 there are the two 2-dim Weyl spinors and the one 4-dim vec representation.

so(8) is special, since the dim of the two spin reps and the one vec rep is ithe same, 8.

Now, how do these two spinors look for so(8)?

They say triality gives the symmetry of Spin(8), not of so(8), it is an automorphism of Spin(8). What does that mean?

Thank you
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,847
967

Related Threads on Anybody here who could explain to me in the simplest terms what is so

Replies
6
Views
2K
Replies
6
Views
2K
  • Last Post
Replies
3
Views
4K
Replies
3
Views
3K
Replies
3
Views
2K
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
4
Replies
93
Views
22K
Replies
1
Views
8K
Top