Signature Characters of Highest-Weight Representations of U[subscript q](l[subscript n]

We consider U[subscript q](l[subscript n), the quantum group of type A for |q| = 1, q generic. We provide formulas for signature characters of irreducible finite-dimensional highest weight modules and Verma modules. In both cases, the technique involves combinatorics of the Gelfand-Tsetlin bases. As an application, we obtain information about unitarity of finite-dimensional irreducible representations for arbitrary q: we classify the continuous spectrum of the unitarity locus. We also recover some known results in the classical limit q→1 that were obtained by different means. Finally, we provide several explicit examples of signature characters