Quantum group of type A and representations of queer Lie superalgebra

We establish a maximal parabolic version of the Kazhdan–Lusztig conjecture [10, Conjecture 5.10] for the BGG category O_k,ζ of q(n)-modules of “±ζ-weights”, where k≤n and ζ∈C∖Z. As a consequence, the irreducible characters of these q(n)-modules in this maximal parabolic category are given by the Kazhdan–Lusztig polynomials of type A Lie algebras. As an application, closed character formulas for a class of q(n)-modules resembling polynomial and Kostant modules of the general linear Lie superalgebras are obtained.