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Q & A: Weyl group

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Most recent answer: 12/04/2015
Q:
Hi.I have got a problem with with weyl reflection and weyl group (the group of weyl reflections).it is said that the weyl group for su3 has 6 members and is isomorphic to s3 but I think since there are pairs of roots with a common normal, weyl reflection with respect to them is the same, in other words I think the weyl group for su3 has got 3 members.please help!
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A:

I haven't ever studied the Weyl group so I ran this by my friend Mike Stone:

The generators are a pair of reflections in planes 120 dgrees apart. The product of these is  a rotation  through  2*120 =240 =-120 degrees. Its inverse is a rotation of +120. A conjugation gives another reflection in the third plane. Then there is the identity.  I think that is 6 elements.

Mike W.


(published on 12/04/2015)

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