2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64445The 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 $\mathfrak{q}(n)$.Version 2: some minor corrections and updated referencesRepresentation Theory17B10text