Signature Characters of Highest-Weight Representations of U[subscript q](𝖌l[subscript n]
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. A...
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| Format: | Article |
| Language: | English |
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Springer-Verlag
2017
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| Online Access: | http://hdl.handle.net/1721.1/109237 https://orcid.org/0000-0002-7968-3291 |
| _version_ | 1826200913199497216 |
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| author | Venkateswaran, Vidya |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Venkateswaran, Vidya |
| author_sort | Venkateswaran, Vidya |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:43:41Z |
| format | Article |
| id | mit-1721.1/109237 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:43:41Z |
| publishDate | 2017 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/1092372022-09-27T21:31:55Z Signature Characters of Highest-Weight Representations of U[subscript q](𝖌l[subscript n] Venkateswaran, Vidya Massachusetts Institute of Technology. Department of Mathematics Venkateswaran, Vidya 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. 2017-05-22T12:30:02Z 2017-05-22T12:30:02Z 2016-01 2015-05 2016-08-18T15:19:54Z Article http://purl.org/eprint/type/JournalArticle 1386-923X 1572-9079 http://hdl.handle.net/1721.1/109237 Venkateswaran, Vidya. "Signature Characters of Highest-Weight Representations of U[subscript q](𝖌l[subscript n]." Algebras and Representation Theory (2016) 19:473–487. https://orcid.org/0000-0002-7968-3291 en http://dx.doi.org/10.1007/s10468-015-9584-1 Algebras and Representation Theory 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. Springer Science+Business Media Dordrecht application/pdf Springer-Verlag Springer Netherlands |
| spellingShingle | Venkateswaran, Vidya Signature Characters of Highest-Weight Representations of U[subscript q](𝖌l[subscript n] |
| title | Signature Characters of Highest-Weight Representations of U[subscript q](𝖌l[subscript n] |
| title_full | Signature Characters of Highest-Weight Representations of U[subscript q](𝖌l[subscript n] |
| title_fullStr | Signature Characters of Highest-Weight Representations of U[subscript q](𝖌l[subscript n] |
| title_full_unstemmed | Signature Characters of Highest-Weight Representations of U[subscript q](𝖌l[subscript n] |
| title_short | Signature Characters of Highest-Weight Representations of U[subscript q](𝖌l[subscript n] |
| title_sort | signature characters of highest weight representations of u subscript q 𝖌l subscript n |
| url | http://hdl.handle.net/1721.1/109237 https://orcid.org/0000-0002-7968-3291 |
| work_keys_str_mv | AT venkateswaranvidya signaturecharactersofhighestweightrepresentationsofusubscriptqglsubscriptn |