Talk:F4 (mathematics)

F4 lattice?
Is this the same as the icositetrachoronic tetracomb with Schläfli symbol {3,4,3,3}? Tom Ruen 17:01, 5 June 2007 (UTC)


 * No, the vertices of {3,4,3,3} do not form a lattice. Rather, the vertices of the dual {3,3,4,3} form an F_4 lattice. The situation is analogous to the two-dimensional cases {6,3} and {3,6}. -- Fropuff 16:45, 6 June 2007 (UTC)


 * Thanks! Good to know. Is it worth linking to hexadecachoronic tetracomb {3,3,4,3}? Or equally I wonder - should F4 lattice instead be redirect to this honeycomb? Tom Ruen 18:23, 6 June 2007 (UTC)

And the third one is the second one
"There are 3 real forms: a compact one, a split one, and a third one."

Sorry but to me that is a very funny sentence! Moon Oracle (talk) 18:28, 10 April 2012 (UTC)


 * Maybe I was the one who wrote this. If so, I guess I couldn't find a better way to phrase it: there are three real forms of F4, one of them is remarkable in that it is the compact form, another is remarkable in that it is the split form, and the third form doesn't have such a convenient one-word description.  Feel free to rewrite more eloquently. ;-) (Of course, we should really be writing a full section on real forms and describe them in some detail.) --Gro-Tsen (talk) 21:44, 10 April 2012 (UTC)

Invariant polynomials
I deleted the two sentences from current version of the page (28 October 2014): "F_4 is the only exceptional lie group which gives the automorphisms of a set of real commutative polynomials. (The other exceptional lie groups require anti-commutative polynomial invariants)." This is not true: for example, the 3875-dimensional irreducible representation of E8 has an invariant quadratic form and an invariant cubic polynomial, and the subgroup of GL3875 stabilizing these two polynomials is exactly E8. Exceptg (talk) 18:38, 28 October 2014 (UTC)


 * Ah, I always found this statement suspicious, but I wasn't sure enough to remove it. I'm glad to know my suspicion was founded.  But is something like what was claimed perhaps true for the lowest-dimensional faithful representation?  Also, does your statement about the 3875-dimensional representation of E₈ follow from an explicit computation, or is it a standard fact, or what?  If you have references about this sort of things, maybe you could add them to the article (and its relatives about the other exceptional Lie groups).  --Gro-Tsen (talk) 11:13, 10 November 2014 (UTC)


 * Well if it is true then it is very new stuff. I found this paper http://arxiv.org/pdf/1309.6611.pdf which is dated 28 April 2015 (two weeks ago!) — Preceding unsigned comment added by 94.119.106.25 (talk) 17:17, 12 May 2015 (UTC)