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Communications in Mathematical Physics

, Volume 199, Issue 3, pp 605–647 | Cite as

Elliptic Algebra \(\): Drinfeld Currents and Vertex Operators

  • Michio Jimbo
  • Hitoshi Konno
  • Satoru Odake
  • Jun'ichi Shiraishi

Abstract:

We investigate the structure of the elliptic algebra \(\) introduced earlier by one of the authors. Our construction is based on a new set of generating series in the quantum affine algebra \(\), which are elliptic analogs of the Drinfeld currents. They enable us to identify \(\) with the tensor product of \(\) and a Heisenberg algebra generated by P,Q with [Q,P]=1. In terms of these currents, we construct an L operator satisfying the dynamical RLL relation in the presence of the central element c. The vertex operators of Lukyanov and Pugai arise as “intertwiners” of \(\) for the level one representation, in the sense to be elaborated on in the text. We also present vertex operators with higher level/spin in the free field representation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Michio Jimbo
    • 1
  • Hitoshi Konno
    • 2
  • Satoru Odake
    • 3
  • Jun'ichi Shiraishi
    • 4
  1. 1.Division of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan.¶E-mail: jimbo@kusm.kyoto-u.ac.jpJP
  2. 2.Department of Mathematics, Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima 739-8521, Japan. E-mail: konno@mis.hiroshima-u.ac.jp JP
  3. 3.Department of Physics, Faculty of Science, Shinshu University, Matsumoto 390-8621, Japan.¶E-mail: odake@azusa.shinshu-u.ac.jpJP
  4. 4.Institute for Solid State Physics, University of Tokyo, Tokyo 106-0032, Japan.¶E-mail: shiraish@momo.issp.u-tokyo.ac.jp}JP

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