Multiplikatorsysteme und Charaktere Hermitescher Modulgruppen

Abstract

We consider the hermitian modular group U(2n, o),n≥2, over an arbitrary imaginary-quadratic number field of discriminantd. By K-theoretic methods it is known that SU(2n, o) is generated by elementary matrices. Therefore, it is easy to determine the factor commutator group and all abelian characters of U(2n, o). Apart from characters which come via the determinant from non-trivial units, there is only one other non-trivial character of U(2n, o) in those cases wheren=2,d≡0 mod 4. This character arises in the same way as for Siegel's modular group Sp(4, ℤ) by an action of U(4, o) on odd theta characteristics.