Communications in Mathematical Physics

, Volume 239, Issue 3, pp 405–447 | Cite as

The Elliptic Algebra and the Drinfeld Realization of the Elliptic Quantum Group

Article
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Abstract

By using the elliptic analogue of the Drinfeld currents in the elliptic algebra , we construct a L-operator, which satisfies the RLL-relations characterizing the face type elliptic quantum group . For this purpose, we introduce a set of new currents \(K_j(v) (1\leq j\leq N)\) in . As in the N=2 case, we find a structure of as a certain tensor product of and a Heisenberg algebra. In the level-one representation, we give a free field realization of the currents in . Using the coalgebra structure of and the above tensor structure, we derive a free field realization of the -analogue of -intertwining operators. The resultant operators coincide with those of the vertex operators in the \(A_{N-1}^{(1)}\)-type face model.

Keywords

Tensor Product Resultant Operator Quantum Group Vertex Operator Tensor Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of MathematicsCollege of Science and Technology, Nihon UniversityChiyoda-ku, TokyoJapan
  2. 2.Department of MathematicsFaculty of Integrated Arts and Sciences, Hiroshima UniversityHigashi-HiroshimaJapan
  3. 3.Department of MathematicsHeriot-Watt UniversityEdinburghUK

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