Résume | Let $G$ be a finite general linear, unitary or symplectic group. The Weil-Steinberg character of $G$ is the product of a Weil character of $G$ with its Steinberg character. The interest to study this character arose from a joint paper with Jianbei An. In joint work with Alexander Zalesski we have shown that the Weil-Steinberg character is multiplicity free for the unitary and symplectic groups. In my talk I will discuss this result, its motivation and some consequences. |