Abstract
We consider \(U_{q}(\mathfrak {gl}_{n})\), 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 \(q \rightarrow 1\) that were obtained by different means. Finally, we provide several explicit examples of signature characters.
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Presented by Vyjayanthi Chari.
Research supported by NSF Mathematical Sciences Postdoctoral Research Fellowship DMS-1204900
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Venkateswaran, V. Signature Characters of Highest-Weight Representations of \(U_{q}(\mathfrak {gl}_{n})\) . Algebr Represent Theor 19, 473–487 (2016). https://doi.org/10.1007/s10468-015-9584-1
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DOI: https://doi.org/10.1007/s10468-015-9584-1