Multiplier systems and characters for Hermitian modular groups (Q1265688)

For an imaginary quadratic field \(K\) of discriminant \(d\) and ring of integers \(R\), we consider the special unitary modular group \(SU (2n,R)\), \(n\geq 2\). The author proves that the only abelian character of \(SU (2n,R)\) is the trivial one except for the case when \(n=2\), in which another nontrivial character exists. In this way one obtains all the multiplier systems of \(SU(2n,R)\). After that the result is easily extended to the unitary modular group \(U(2n,R)\).