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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2016
Hauptverfasser: Fu, Y., Shelley-Abrahamson, S.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2016
Online Zugang:https://nasplib.isofts.kiev.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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-147751
record_format dspace
spelling Fu, Y.
Shelley-Abrahamson, S.
2019-02-15T19:09:31Z
2019-02-15T19:09:31Z
2016
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
https://nasplib.isofts.kiev.ua/handle/123456789/147751
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.
A portion of this work was conducted at the 2015 MIT Summer Program in Undergraduate Research and the MIT Undergraduate Research Opportunities Program, for which the second author was a graduate student mentor. We thank Pavel Etingof for many useful discussions and for suggesting the direction of this work. We also thank the anonymous referees for their valuable remarks and suggestions.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank
spellingShingle A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank
Fu, Y.
Shelley-Abrahamson, S.
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
author Fu, Y.
Shelley-Abrahamson, S.
author_facet Fu, Y.
Shelley-Abrahamson, S.
publishDate 2016
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.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.
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