# Talk:Weyl group

WikiProject Mathematics (Rated Start-class, Mid-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 Start Class
 Mid Importance
Field:  Algebra

## inconsistent definition

There is something that I do not understand. It looks to me, from the picture, that if I choose the hyperplane v^ to be above the root gamma, then the system of positive roots will change because it will now include -gamma and not gamma anymore. Therefore, the positive roots may change even if v^ stays in the same hyperplane. Isn't then better to say the weyl chambers are those portion of the plane delimited by the half lines generated by two roots?

Alberto

The article is correct. Roots and Weyl chambers/v live in spaces *dual* one to each other. Think of what happens in higher dimension to vectors, roots, hyperplanes...

## Weyl group of A2 has only order 6

Root system claims that the Weyl group associated to A_n hat (n+1)! elements. I haven't checked this myself, but at least for n=2 they seem to be right: The hexagon has 3 diagonals meeting at its center. The reflections on these diags genearate the dihedral group of the equilateral triangle. Rgds --Boobarkee (talk) 13:56, 7 July 2009 (UTC)

The Weyl group associated to A_n is the symmetric group on n+1 points and has (n+1)! elements. I have no idea what the intro to this article was talking about, but I deleted the incorrect statement. JackSchmidt (talk) 14:10, 7 July 2009 (UTC)

## Two different definitions

I am under the impression that there is a definition of the Weyl group of a root system and a definition of a Weyl group of a split reductive algebraic group with a given maximal torus, and the fact that these two coincide is a theorem. I think it would be useful to state both definitions. As it stands, it's a bit strange that the section on Bruhat Decomposition gives a completely different definition of the Weyl group.

Owen Jones (talk) 14:53, 10 November 2009 (UTC)

## there is no definition

In this article of wikipedia there is no definition of a weyl group. only different perspectives how to see it. what about N_G(T)/T as definition? —Preceding unsigned comment added by 132.230.30.96 (talk) 14:49, 13 January 2010 (UTC)

## Relation to Conformal Group?

There seems to be a relation between Weyl symmetry and Conformal symmetry. Is there also a relation between a Weyl group and a Conformal group? My hunch would be yes. Can't find it in the article, though. 70.247.162.34 (talk) 04:16, 30 September 2014 (UTC)