Abstract
The purpose of this Letter is to define and construct highest weight modules for Felder's elliptic quantum groups. This is done by using exchange matrices for intertwining operators between modules over quantum affine algebras.
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References
Chari, V. and Pressley, A.: A Guide to Quantum Groups, Cambridge University Press, 1995.
Etingof, P., Frenkel, I. and Kirillov A.: Lectures on Representation Theory and the Knizhnik–Zamolodchikov Equations, Amer. Math. Soc., Providence, 1998.
Etingof, P. and Schiffmann, O.: A link between two elliptic quantum groups, Asian J. Math, 2(2), (1998), 345–354; Preprint, Providence, math/9801108.
Etingof, P. and Varchenko, A.: Solutions of the quantum dynamical Yang–Baxter equation and dynamical quantum groups, Comm. Math. Phys. (1998).
Etingof, P. and Varchenko, A.: Exchange dynamical quantum groups, Preprint math/9801135.
Felder, G.: Elliptic quantum groups, Preprint hep-th/9412207, Proc. ICMP, Paris (1994).
Foda, O., Iohara, K., Jimbo, M., Kedem, R., Miwa, T. and Yan, H.: An elliptic quantum algebra for sl2 2, Lett. Math. Phys. 32(3) (1994), 259–268.
Frenkel, I. and Reshetikhin, N.: Quantum affine algebras and holonomic difference equations, Comm. Math. Phys. 146(1) (1992), 1–60.
Jimbo, M., Konno, H., Odake, S. and Shiraishi, J.: Quasi-Hopf twistors for elliptic quantum groups, Preprint q-alg/9712029.
Kac, V.: Infinite-Dimensional Lie Algebras, 3rd edn, Cambridge University Press, 1995.
Kazhdan, D. and Soibelman, Y.: Representations of quantum affine algebras, Selecta Math. (N.S.) 1(3) (1995), 537–595.
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Etingof, P., Schiffmann, O. On Highest Weight Modules Over Elliptic Quantum Groups. Letters in Mathematical Physics 47, 179–188 (1999). https://doi.org/10.1023/A:1007543104904
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DOI: https://doi.org/10.1023/A:1007543104904