Title: A counterexample to a conjecture of Kiyota, Murai and Wada,
Abstract: Kiyota, Murai and Wada conjectured in 2002 that the largest eigenvalue of the
Cartan matrix C of a block of a finite group is rational if and only if all
eigenvalues of C are rational. We provide a counterexample to this conjecture
and discuss related questions.