Talk:SO(8)

Triality is nowhere defined. It needs to be defined before other things about it are mentioned
The first mentions of triality are as follows:

"This gives rise to peculiar feature of Spin(8) known as triality. Related to this is the fact that the two spinor representations, as well as the fundamental vector representation, of Spin(8) are all eight-dimensional (for all other spin groups the spinor representation is either smaller or larger than the vector representation). The triality automorphism of Spin(8) lives in the outer automorphism group of Spin(8) which is isomorphic to the symmetric group S3 that permutes these three representations."

Totally inappropriate. Will someone knowledgeable about triality please make sure that triality is defined before additional things about it are mentioned? (Also, there should be a comma after "SO(8)" above.)Daqu (talk) 03:41, 8 August 2014 (UTC)

Bad judgment
In the Triality section, this sentence appears with no prior mention of any automorphism of Spin(8) or of anything else:

"The triality automorphism of Spin(8) lives in the outer automorphism group of Spin(8) which is isomorphic to the symmetric group S3 that permutes these three representations."

Yes, this section does begin with the notice "Main article: Triality". But that in no way substitutes for this article saying what it is talking about. You cannot refer to "the" triality automorphism if we don't yet know that there is even one of them.

Above all because this article has not yet hinted at what the word "triality" means. Sure, maybe a reader can figure it out from the symmetry of the Dynkin diagram. But it is very bad judgment to just assume that either a) the reader knows what a "triality automorphism" is or b) they ought to go read the Triality article before reading this section.

(Also, the sentence above needs a comma after "Spin(8)".)2600:1700:E1C0:F340:8D04:C989:2E0F:8168 (talk) 21:34, 14 December 2018 (UTC)