Rational and trigonometric degeneration of the double affine Hecke algebra of type $A$

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dc.creatorSuzuki, Takeshi
dc.date2005-02-25
dc.date2005-08-08
dc.date.accessioned2026-07-07T05:17:29Z
dc.date.available2026-07-07T05:17:29Z
dc.descriptionWe study a connection between the representation theory of the rational Cherednik algebra of type $GL_n$ and the representation theory of the degenerate double affine Hecke algebra (the degenerate DAHA). We focus on an algebra embedding from the rational Cherednik algebra to the degenerate DAHA and investigate the induction functor through this embedding. We prove that this functor embeds the category ${\mathcal O}$ for the rational Cherednik algebra fully faithfully into the category ${\mathcal O}$ for the degenerate DAHA. We also study the full subcategory ${\mathcal O}^{ss}$ of ${\mathcal O}$ consisting of those modules which are semisimple with respect to the commutative subalgebra generated by Cherednik-Dunkl operators. A classification of all irreducible modules in ${\mathcal O}^{ss}$ for the rational Cherednik algebra is obtained from the corresponding result for the degenerate DAHA.
dc.description13 pages. In ver.2, some notation and wording were changed, and several typos and minor errors were corrected
dc.identifierhttps://arxiv.org/abs/math/0502534
dc.identifierhttp://arxiv.org/abs/math/0502534
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74320
dc.subjectRepresentation Theory
dc.subjectQuantum Algebra
dc.titleRational and trigonometric degeneration of the double affine Hecke algebra of type $A$
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