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July 2016 Higher level representation of the elliptic quantum group $U_{q,p}(\widehat{\mathfrak{sl}}_2)$ and its integrability
Rasha Mohamed Farghly
Hiroshima Math. J. 46(2): 163-185 (July 2016). DOI: 10.32917/hmj/1471024947

Abstract

By using an elliptic analogue of the Drinfeld coproduct, we construct the level-$(k+1)$ representation of the elliptic quantum group $U_{q,p}(\widehat{\mathfrak{sl}}_2)$ from the level-1 highest weight representation. The quantum Z-algebra of level-$(k+1)$ is realized. We also find the elliptic analogue of the condition of integrability for higher level modules constructed by the Drinfeld coproduct. This also enables us to express $\Delta^k(e(z))\Delta^k(e(zq^2))\dots\Delta^k(e(zq^{2(N-1)}))$ and $\Delta^k(f(z))\Delta^k(f(zq^2))\Delta^k(f(zq^{-2}))\dots\Delta^k(f(zq^{-2(N-1)}))$ as vertex operators of the level-$(k+1)$ bosons.

Citation

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Rasha Mohamed Farghly. "Higher level representation of the elliptic quantum group $U_{q,p}(\widehat{\mathfrak{sl}}_2)$ and its integrability." Hiroshima Math. J. 46 (2) 163 - 185, July 2016. https://doi.org/10.32917/hmj/1471024947

Information

Received: 18 March 2015; Revised: 26 February 2016; Published: July 2016
First available in Project Euclid: 12 August 2016

zbMATH: 1378.17028
MathSciNet: MR3536994
Digital Object Identifier: 10.32917/hmj/1471024947

Subjects:
Primary: 12A34, 98B76
Secondary: 23C57

Rights: Copyright © 2016 Hiroshima University, Mathematics Program

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Vol.46 • No. 2 • July 2016
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