Representations of quantum tori and double-affine Hecke algebras

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dc.creatorBaranovsky, Vladimir
dc.creatorEvens, Sam
dc.creatorGinzburg, Victor
dc.date2000-05-02
dc.date.accessioned2026-07-07T04:34:58Z
dc.date.available2026-07-07T04:34:58Z
dc.descriptionWe study a BGG-type category of infinite dimensional representations of H[W], a semi-direct product of the quantum torus with parameter `q' built on the root lattice of a semisimple group G, and the Weyl group of G. Irreducible objects of our category turn out to be parameterized by semistable G-bundles on the elliptic curve C^*/q^Z. In the second part of the paper we construct a family of algebras depending on a parameter `v' that specializes to H[W] at v=0, and specializes to the double-affine Hecke algebra introduced by Cherednik, at v=1. We propose a Deligne-Langlands-Lusztig type conjecture relating irreducible modules over the double-affine Hecke algebra to Higgs G-bundles on the elliptic curve. The conjecture may be seen as a natural `v-deformation' of the classification of simple H[W]-modules obtained in the first part of the paper. Also, an `operator realization' of the double-affine Hecke algebra, as well as of its Spherical subalgebra, in terms of certain `zero-residue' conditions is given.
dc.descriptionLaTeX, 33 pages
dc.identifierhttps://arxiv.org/abs/math/0005024
dc.identifierhttp://arxiv.org/abs/math/0005024
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59112
dc.subjectRepresentation Theory
dc.subjectAlgebraic Geometry
dc.subjectQuantum Algebra
dc.titleRepresentations of quantum tori and double-affine Hecke algebras
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