The Elliptic Algebra and the Drinfeld Realization of the Elliptic Quantum Group |
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Authors: | Takeo?Kojima Email author" target="_blank">Hitoshi?KonnoEmail author |
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Institution: | (1) Department of Mathematics, College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo, 101-0062, Japan;(2) Department of Mathematics, Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japan;(3) Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, UK |
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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 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 -type face model. |
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