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Results tagged with weyl-group
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user 22846
The Weyl group of a root system is a subgroup generated by reflections through the hyperplanes orthogonal to the roots.
8
votes
Accepted
When the longest element of Weyl group is rational?
Let $B$ be a Borel subgroup containing $T$. As $F(B)$ and $B$ are both Borel subgroups containing $T$ there exists an element $n \in N_G(T)$ such that ${}^nF(B) = B$. Thus the Frobenius endomorphism $ …
- 2,902
6
votes
Accepted
For a Weyl group, what is the connection between its exponents and lengths of its elements?
I would leave this as a comment but I don't appear to have enough reputation points for that. Just to add to Philippe's answer that you will also find this as Theorem 10.2.3 in Carter's "Simple Groups …
- 2,902
5
votes
Accepted
Is this characterization of (-1)-eigenspaces of the Weyl group of $E_6$ known?
EDIT II: Sorry to bump this again but the answer to this question can be phrased entirely in terms of finite Coxeter groups and doesn’t depend at all on the fact that we’re dealing with $\textsf{E}_6$ …
- 2,902