Character of finite dimensional irreducible \(q(n)\)-modules (Q1366504)

The problem of finding the characters of all irreducible finite-dimensional representations of any classical simple Lie superalgebra was posed by Kac in 1977 [\textit{V. G. Kac}, Lect. Notes Math. 676, 597-626 (1978; Zbl 0388.17002)]. Since then, there have been many partial solutions, especially for the general linear Lie superalgebra \(gl(m/n)\). Recently, one of the authors [\textit{V. Serganova}, Sel. Math., New Ser. 2, 607-651 (1996; Zbl 0881.17005)] has solved the character problem for \(gl(m/n)\) by finding a method to determine the composition factors of a so-called Kac module. In this paper, the solution is announced for the ``queer'' series of Lie superalgebras \(q(n)\). The method to determine the characters is described in detail, but the actual proofs will appear elsewhere. The algorithm to find characters is illustrated for all finite-dimensional irreducible representations of \(q(n)\) for \(n\leq 4\).