Restricting the Steinberg character in finite symplectic groups

Abstract. We determine the restriction of the Steinberg character of a -nite symplectic group of odd characteristic to its maximal parabolic subgroup stabilizing a line. We relate this restriction to the tensor product of a Weil char-acter with the Steinberg character. As an application we prove that Donovan's conjecture has a positive answer for unipotent `-blocks of the six-dimensional symplectic groups of odd characteristic when `> 3. 1