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We consider $U_{q}(\mathfrak{gl}_{n})$, the quantum group of type $A$ for$|q| = 1$, $q$ generic. We provide formulas for signature characters ofirreducible finite-dimensional highest weight modules and Verma modules. Inboth cases, the technique involves combinatorics of the Gelfand-Tsetlin bases.As an application, we obtain information about unitarity of finite-dimensionalirreducible representations for arbitrary $q$: we classify the continuousspectrum of the unitarity locus. We also recover some known results in theclassical limit $q \rightarrow 1$ that were obtained by different means.Finally, we provide several explicit examples of signature characters.

Signature characters of highest-weight representations of $U_{q}(\mathfrak{gl}_{n})$