Chemistry in disks II. Poor molecular content of the AB Aurigae disk

Aims. We study the molecular content and chemistry of a circumstellar disk surrounding the Herbig Ae star AB Aur at (sub-)millimeter wavelengths. Our aim is to reconstruct the chemical history and composition of the AB Aur disk and to compare it with disks around low-mass, cooler T Tauri stars. Methods: We observe the AB Aur disk with the IRAM Plateau de Bure Interferometer in the C- and D-configurations in rotational lines of CS, HCN, C2H, CH3OH, HCO^+, and