Talk:Complex reflection group

What does it mean?

WP has many articles which aficionados may hold exquisitely clear and precise but which for John Doe using WP for enlightenment may as well be gibberish written in Ge'ez. This is an example from mathematics (where you might argue that 99% of JDs could never get the meaning) but other less cerebral subjects (for example Sports) are written up in their peculiar jargons undefined in the articles.--SilasW (talk) 11:51, 9 January 2008 (UTC)

Brackets

This group looks funny on my browser, with funny wide gaps before and after the brackets:〈3,3,3〉₂. This looks better <3,3,3>₂.

Ok, I don't know what to say about this. The less-than/greater-than signs are quite ugly, by the spacing around them is normal. --JBL (talk) 00:15, 24 June 2016 (UTC)

Infinite Shephard groups?

Finite subgroups of rank 2

Coxeter identifies 8 Rank 2 Shephard groups: δ^2,2
₂=2[∞]2, δ^3,2
₂=3[12]2, δ^4,2
₂=4[8]2, δ^6,2
₂=6[6]2, δ^3,3
₂=3[6]3, δ^6,3
₂=6[4]3, δ^4,4
₂=4[4]4, δ^6,6
₂=6[3]6, listed here Complex_polytope#Regular_complex_apeirogons. Should these infinite groups be added to this article?

I'm also curious about subgroup relations. Comparing to relations he gives to the finite groups (collected here File:Rank2_shephard_subgroups.png), I can see 4[4]4 is an index 2 subgroup of 4[8]2, 3[6]3 is an index 2 subgroup of 3[12]2, 6[3]6 is an index 2 subgroup of 6[6]2, and an index 3 subgroup of 6[4]3. I imagine there are other relations. Does anyone know of any sources for this? Tom Ruen (talk) 06:32, 20 July 2016 (UTC)

I have mixed feelings about the infinite groups. On the second question, in the case of real reflection groups one has for example this paper of Douglass, Pfeiffer and Roehle: http://arxiv.org/abs/1101.5893. I don't know if anything is written down in the complex case. --JBL (talk) 15:54, 20 July 2016 (UTC)

An interesting paper for the real cases. I'm looking specifically at reflective subgroups of the same rank since this can show symmetry relations between polytopes of different symmetry groups. I've not been able to find any sources besides Coxeter who doesn't seem to list subgroup relations, but here's my best known chart including only mirror (node) removal subgroups that work when there are even-order branches. Tom Ruen (talk) 06:52, 23 July 2016 (UTC)