The Berenstein–Zelevinsky quantum cluster algebra conjecture
The Berenstein–Zelevinsky quantum cluster algebra conjecture
We prove the Berenstein–Zelevinsky conjecture that the quantized coordinate rings of the double Bruhat cells of all finite-dimensional connected, simply connected simple algebraic groups admit quantum cluster algebra structures with initial seeds as specified by [5]. We furthermore prove that the corresponding upper quantum cluster algebras coincide with the constructed …