  The problem of computing the characters of the finite dimensional irreducible
representations of the Lie superalgebra $\mathfrak q(n)$ over $\C$ was solved
in 1996 by I. Penkov and V. Serganova. In this article, we give a different
approach relating the character problem to canonical bases of the quantized
enveloping algebra $U_q(\mathfrak b_{\infty})$. We also formulate for the first
time a conjecture for the characters of the infinite dimensional irreducible
representations in the analogue of category $\mathcal O$ for the Lie
superalgebra $\mathfrak{q}(n)$.
