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Galois geometry, finite projective and affine spaces, polar spaces, partial geometries, generalized polygons, near polygons, and other finite incidence geometries.

2 votes
1 answer
182 views

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 $\langl …