Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra q(n)

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The problem of computing the characters of the finite dimensional irreducible representations of the Lie superalgebra q(n) over 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 Uq(b∞). We also formulate for the first time a conjecture for the characters of the infinite dimensional irreducible representations in the analogue of category O for the Lie superalgebra q(n).