Skip to main content
MathOverflow

Return to Question

Post Reopened by José Figueroa-O'Farrill, Ricardo Andrade, Derek Holt, Stefan Kohl♦, S. Carnahan♦
added 63 characters in body
Source Link
Violetta
Violetta
  • 29
  • 2

Is the following statement true for finite reflection groups?

Let $G$ be a finite reflection group acting on $\mathbb{R}^n$, let $x, y\in \mathbb{R}^n$ and let $z$ be in the orbit of $y$. If $\langle x,y\rangle = \langle x, z\rangle$, then there exists $g$ in the stabiliser of $x$ such that $z = gy$.

An important addition: $x$ and $y$ are in the same chamber.

Is the following statement true for finite reflection groups?

Let $G$ be a finite reflection group acting on $\mathbb{R}^n$, let $x, y\in \mathbb{R}^n$ and let $z$ be in the orbit of $y$. If $\langle x,y\rangle = \langle x, z\rangle$, then there exists $g$ in the stabiliser of $x$ such that $z = gy$.

Is the following statement true for finite reflection groups?

Let $G$ be a finite reflection group acting on $\mathbb{R}^n$, let $x, y\in \mathbb{R}^n$ and let $z$ be in the orbit of $y$. If $\langle x,y\rangle = \langle x, z\rangle$, then there exists $g$ in the stabiliser of $x$ such that $z = gy$.

An important addition: $x$ and $y$ are in the same chamber.

Post Closed as "Not suitable for this site" by HJRW, Dima Pasechnik, Stefan Waldmann, Stefan Kohl♦, Chris Godsil
added 5 characters in body
Source Link
Violetta
Violetta
  • 29
  • 2

Is inner product preserved only by athe stabiliser in a finite reflection group?

Is the following statement true for finite reflection groups?

Let $G$ be a finite reflection group acting on $\mathbb{R}^n$, let $x, y\in \mathbb{R}^n$ and let $z$ be in the orbit of $y$. If $\langle x,y\rangle = \langle x, z\rangle$, then there exists $g$ in the stabiliser of $x$ such that $z = gy$.

Is inner product preserved only by a stabiliser in a finite reflection group?

Is the following statement true for finite reflection groups?

Let $G$ be a finite reflection group acting on $\mathbb{R}^n$ $x, y\in \mathbb{R}^n$ and let $z$ be in the orbit of $y$. If $\langle x,y\rangle = \langle x, z\rangle$, then there exists $g$ in the stabiliser of $x$ such that $z = gy$.

Is inner product preserved only by the stabiliser in a finite reflection group?

Is the following statement true for finite reflection groups?

Let $G$ be a finite reflection group acting on $\mathbb{R}^n$, let $x, y\in \mathbb{R}^n$ and let $z$ be in the orbit of $y$. If $\langle x,y\rangle = \langle x, z\rangle$, then there exists $g$ in the stabiliser of $x$ such that $z = gy$.

Source Link
Violetta
Violetta
  • 29
  • 2

Is inner product preserved only by a stabiliser in a finite reflection group?

Is the following statement true for finite reflection groups?

Let $G$ be a finite reflection group acting on $\mathbb{R}^n$ $x, y\in \mathbb{R}^n$ and let $z$ be in the orbit of $y$. If $\langle x,y\rangle = \langle x, z\rangle$, then there exists $g$ in the stabiliser of $x$ such that $z = gy$.