Characters of finite-dimensional irreducible q(n)-modules

The solution of the Kac character problem for the 'queer' series of Lie superalgebras q(n) is announced. An explicit algorithm which computes the character of an arbitrary finite-dimensional irreducible q(n)-module is presented. As an illustration, the 'correction terms' to the generic character formula of Penkov (Monatsh. Math. 118 (1994), 419) are written down for all finite-dimensional irreducible representations of q(n), for n less than or equal to 4, with nongeneric character.