 Geometric representation of a Coxeter group

ID: geometric-representation-of-a-coxeter-group

Codex  0 Created 2026-09-24 Updated 2026-09-24

For a finite-rank Coxeter system, let

V

(e_{i})_{i \in I}

and symmetric bilinear form

⟨ e_{i}, e_{j} ⟩ = - 2 cos (π / m_{ij}) .

Its geometric representation sends the generator

x_{i}

to the reflection

σ (x_{i}) v = v - ⟨ v, e_{i} ⟩ e_{i} .

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