Signature Characters of Highest-Weight Representations of U[subscript q](𝖌l[subscript n]
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10468_2015_Article_9584.pdf
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260.84 KB
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Author(s)
Venkateswaran, Vidya
Date Issued
January 2016
Journal
Algebras and Representation Theory
Publisher
Springer-Verlag
Citation
Venkateswaran, Vidya. "Signature Characters of Highest-Weight Representations of U[subscript q](𝖌l[subscript n]." Algebras and Representation Theory (2016) 19:473–487.
Version
Author's final manuscript
Abstract
We consider U[subscript q](𝖌l[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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10468-015-9584-1
