Talk:Weyl group

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Mathematics rating:	Stub Class	Mid Priority	Field: Algebra
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Needs more structure and explanation. Geometry guy 16:00, 22 May 2007 (UTC)

[edit] 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...