research

Quantum toroidal algebras and their representations

Abstract

Quantum toroidal algebras (or double affine quantum algebras) are defined from quantum affine Kac-Moody algebras by using the Drinfeld quantum affinization process. They are quantum groups analogs of elliptic Cherednik algebras (elliptic double affine Hecke algebras) to whom they are related via Schur-Weyl duality. In this review paper, we give a glimpse on some aspects of their very rich representation theory in the context of general quantum affinizations. We illustrate with several examples. We also announce new results and explain possible further developments, in particular on finite dimensional representations at roots of unity.Comment: 24 pages. To appear in Selecta Mathematic

    Similar works

    Full text

    thumbnail-image

    Available Versions

    Last time updated on 19/12/2019