List questions from coxeter-groups

Published on 16 Apr 2026 - 6:31

201

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Why $W(B_\ell) \simeq (\Bbb Z/2\Bbb Z)^\ell \rtimes S_\ell$?

Published on 17 Apr 2026 - 5:55

152

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Finite reflection groups in a Euclidean space

Published on 13 Apr 2026 - 10:43

63

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In type $B_n$, is $s_\beta(\alpha)=\alpha+\sqrt{2}\beta$?

Published on 15 Apr 2026 - 19:55

103

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In the dihedral group $D_{2m}$ for $m$ odd, does conjugation by $w_0$ exchange the simple reflections?

Published on 15 Apr 2026 - 14:57

1.3k

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Finding the longest element $w_0$ of the reflection group $S_n$ with respect to the positive system $\{e_i - e_j, 1≤i < j≤1\}$

Published on 12 Apr 2026 - 19:01

88

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Reduced word labeling of Bruhat Order

Published on 13 Apr 2026 - 20:23

398

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Slick proof that Coxeter groups $H_3$ and $H_4$ are finite?

Published on 13 Apr 2026 - 6:56

357

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Confusing notation: Presentation theory of symmetric groups (Coxeter presentations)

Published on 14 Apr 2026 - 15:42

53

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A interesting number game in a lecture note about coxeter group

Published on 12 Apr 2026 - 18:33

630

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Is there a root system for a Dihedral group?

Published on 08 Apr 2026 - 23:34

48

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How to prove that $T_L(u) = T_L(w)$ implies that $u=w$?

Published on 14 Apr 2026 - 17:53

64

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A question about long roots and their behaviour under the scalar product

Published on 10 Apr 2026 - 6:09

65

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Computing orders of some irreducible finite Coxeter groups

Published on 13 Apr 2026 - 7:27

129

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Condition implying $N(H)/H$ a Coxeter group?

Published on 25 Mar 2026 - 14:27

List Question

Why does $P_JnP_K\cap N=N_JnN_K$ in a group with split $BN$-pair?

Why $W(B_\ell) \simeq (\Bbb Z/2\Bbb Z)^\ell \rtimes S_\ell$?

Finite reflection groups in a Euclidean space

In type $B_n$, is $s_\beta(\alpha)=\alpha+\sqrt{2}\beta$?

In the dihedral group $D_{2m}$ for $m$ odd, does conjugation by $w_0$ exchange the simple reflections?

Finding the longest element $w_0$ of the reflection group $S_n$ with respect to the positive system $\{e_i - e_j, 1≤i < j≤1\}$

Reduced word labeling of Bruhat Order

Slick proof that Coxeter groups $H_3$ and $H_4$ are finite?

Confusing notation: Presentation theory of symmetric groups (Coxeter presentations)

A interesting number game in a lecture note about coxeter group

Is there a root system for a Dihedral group?

How to prove that $T_L(u) = T_L(w)$ implies that $u=w$?

A question about long roots and their behaviour under the scalar product

Computing orders of some irreducible finite Coxeter groups

Condition implying $N(H)/H$ a Coxeter group?

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