**Speaker:** Rafał Lutowski (Gdańsk)

**Title:** * Irreducible Euclidean Representations of the Fibonacci Groups*

**Abstract:**

We show that for every n ≥ 5 and every Hantzsze-Wendt group Γ of dimension n there exists a representation

Φ : F(n-1,2n) → O(n) ⋉ ℝ^{n}

of the Fibonacci group F(n-1,2n), such that the image of Φ is equal to Γ. The main idea used in the proof is the decomposition of Φ into irreducible constituents, which is quite interesting because of the non-linearity of this representation.