Representations of Quantum Tori and G-bundles on Elliptic Curves

  • Vladimir Baranovsky
  • Sam Evens
  • Victor Ginzburg
Part of the Progress in Mathematics book series (PM, volume 213)


We study a BGG-type category of infinite-dimensional representations of H[W]a semidirect product of the quantum torus with parameter q, built on the root lattice of a semisimple group Gand the Weyl group of G. Irreducible objects of our category turn out to be parametrized by semistable G-bundles on the elliptic curve C*/qZ.

Keywords and phrases

nilpotent coadjoint orbit Dixmier algebra symplectic reduction 


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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Vladimir Baranovsky
    • 1
  • Sam Evens
    • 2
  • Victor Ginzburg
    • 3
  1. 1.Department of Mathematics 253–37CaltechPasadenaUSA
  2. 2.Department of MathematicsUniversity of Notre DameNotre DameUSA
  3. 3.Department of MathematicsUniversity of ChicagoChicagoUSA

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