All Questions
Tagged with group-theory coxeter-groups
127
questions
1
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2
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341
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List of all elements of the Weyl group of type $C_3$.
What is the list of all elements of the Weyl group of type $C_3$ in terms of simple refletions $s_1, s_2, s_3$? There are 48 elements in the group. Thank you very much.
- 14.6k
2
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0
answers
1k
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Significance of deletion and exchange conditions in reflection groups
I am having trouble warping my head around the exchange and deletion conditions in finite reflection groups (i.e.Coxeter groups).
It is mentioned as the characterising property of coxeter groups among ...
- 388
3
votes
1
answer
1k
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Converting a (signed) permutation to a reduced word
I vaguely know that by looking at the inversions of a permutation, you can write down the reduced word expressing the permutation as a product of adjacent transpositions $s_i = (i,i+1)$. However, I ...
- 55.9k
1
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0
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77
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Doubt in the proof of Conjugacy of positive systems under reflection group
I am stuck at a small thing in the proof of conjugacy of positive systems under a finite reflection group. I am using the notation and definitions used in the text by James E. Humphreys. I reproduce ...
- 388
10
votes
1
answer
249
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Description of flipping tableau for inversions in reduced decompositions of permutations
Short version: Is there a graphical description of the possible orders in which inversions can appear in a reduced decomposition of a permutation?
Something akin to the definition of standard Young ...
- 55.9k
7
votes
2
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1k
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Reflection groups and symmetric group
Define the action of $S_n$ on $\mathbb{R}^n$:
take any $x\in S_n$, consider the mapping $x: \mathbb{R}^n\to\mathbb{R}^n$, $e_1, e_2 ...e_n$ are the standard basis of $\mathbb{R}^n$, $x(e_k)=e_{x(k)}$...
- 93
15
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2
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Finite/Infinite Coxeter Groups
In the same contest as this we got the following problem:
We are given a language with only three letters letters $A,B,C$. Two words are equivalent if they can be transformed from one another using ...
- 23.5k