All Questions
6
questions
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How to find the longest element in a double coset of a Weyl group using SageMath?
I asked a question about computing longest element in a double coset in AskSage
It has not been answered for a long time. So I asked it here.
Let $W$ be a finite Coxeter group. Denote by $W_I$ the ...
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1
vote
1
answer
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Defining the Weyl group of type $D_n$ as a subgroup of Weyl group of type $B_n$ in GAP
I am looking to define the Weyl group of type $D_n$ as a subgroup of Weyl group of type $B_n$ in the software GAP. In general, one can define these groups separately. For example, let's say
...
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1
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1
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Longest element of $D_n$ and the set of positive roots [duplicate]
Personally I am not very familiar with group theory and need some clarifications.
Let's look at $D_n$ and its longest elemements.
According to OEIS A162206 the triangle begins:
$1$;
$1;2;1$;
$1;3;5;6;...
3
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0
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Question about a certain involution on a Coxeter group $W$.
This is a small question that arose while reading the paper On Okuyama's Theorems About Alvis-Curtis Duality by M. Cabanes. It can be read here.
Let $(W,S)$ be a finite Coxeter system, $l$ the length ...
- 12.4k
1
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555
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About parabolic subgroup of a Weyl group
Let $W$ be a Weyl group/Coxeter group. Let $\Phi$ be the associated root system, fix a positive root system $\Phi^+$ and let
$\Delta$ be the set of simple roots.
Let $W_I$ be the parabolic subgroup ...
- 255
0
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How to justify that any set of coxeter generators for a Weyl group are simple
Let $G$ be a group with a $\mathrm{BN}$-pair, and let $W:=N/(B\cap N)$ be the Weyl group of $G$, where $W$ is generated by a set $S$ of simple roots (as in the definition of a $\mathrm{BN}$-pair) and $...
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