A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank
We give explicit constructions of some finite-dimensional representations of generalized double affine Hecke algebras (GDAHA) of higher rank using R-matrices for Uq(slN). Our construction is motivated by an analogous construction of Silvia Montarani in the rational case. Using the Drinfeld-Kohno the...
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2016
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147751 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank / Y. Fu, S. Shelley-Abrahamson // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 15 назв. — англ. |
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irk-123456789-1477512019-02-16T01:25:15Z A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank Fu, Y. Shelley-Abrahamson, S. We give explicit constructions of some finite-dimensional representations of generalized double affine Hecke algebras (GDAHA) of higher rank using R-matrices for Uq(slN). Our construction is motivated by an analogous construction of Silvia Montarani in the rational case. Using the Drinfeld-Kohno theorem for Knizhnik-Zamolodchikov differential equations, we prove that the explicit representations we produce correspond to Montarani's representations under a monodromy functor introduced by Etingof, Gan, and Oblomkov. 2016 Article A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank / Y. Fu, S. Shelley-Abrahamson // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 15 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 20C08 DOI:10.3842/SIGMA.2016.055 http://dspace.nbuv.gov.ua/handle/123456789/147751 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We give explicit constructions of some finite-dimensional representations of generalized double affine Hecke algebras (GDAHA) of higher rank using R-matrices for Uq(slN). Our construction is motivated by an analogous construction of Silvia Montarani in the rational case. Using the Drinfeld-Kohno theorem for Knizhnik-Zamolodchikov differential equations, we prove that the explicit representations we produce correspond to Montarani's representations under a monodromy functor introduced by Etingof, Gan, and Oblomkov. |
| format |
Article |
| author |
Fu, Y. Shelley-Abrahamson, S. |
| spellingShingle |
Fu, Y. Shelley-Abrahamson, S. A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Fu, Y. Shelley-Abrahamson, S. |
| author_sort |
Fu, Y. |
| title |
A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank |
| title_short |
A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank |
| title_full |
A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank |
| title_fullStr |
A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank |
| title_full_unstemmed |
A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank |
| title_sort |
family of finite-dimensional representations of generalized double affine hecke algebras of higher rank |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147751 |
| citation_txt |
A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank / Y. Fu, S. Shelley-Abrahamson // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 15 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2025-07-11T02:46:13Z |
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2025-07-11T02:46:13Z |
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