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A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank
Інший ID:
2010 Mathematics Subject Classification: 20C08
DOI:10.3842/SIGMA.2016.055
DOI:10.3842/SIGMA.2016.055
Посилання:
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.
Підтримка:
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.
Дата:
2016
Переглядів:
699
Завантажень:
272
Анотація:
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.
