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Results tagged with gr.group-theory
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user 37803
Questions about the branch of algebra that deals with groups.
1
vote
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answers
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Standard involutions conjugate to the negative of a standard involution in a Coxeter group
Consider a finite irreducible Coxeter group $W$ with a fixed generator set $S$. Every involution in $W$ is conjugate to a standard involution $c_I$, for some subset $I\subset S$. For example, this st …
2
votes
Standard involutions conjugate to the negative of a standard involution in a Coxeter group
Partial answer
Concerning the particular example in the question, $-c_{\{1\}}$ is conjugate to $c_{\{1,3,4,5\}}$, and $-c_{\{5\}}$ is conjugate to $-c_{\{1,2,3,4\}}$. This can almost be deduced from …
0
votes
Standard involutions conjugate to the negative of a standard involution in a Coxeter group
Here is another approach to identify the conjugay class of the specific involution $-c_{\{1\}}$ in the question. The approach is complementary to my other answer in that it also allows the determina …
3
votes
Reference for embeddings of reflection groups (related to folding ADE Coxeter graphs)?
One reference for these embeddings is the first section of
[Stein] Robert Steinberg, Endomorphisms of linear algebraic groups.
Memoirs of the American Mathematical Society, No. 80
This does not …