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VOL. 76 | 2018 Elliptic quantum groups $U_{q,p}(\widehat{\mathfrak{gl}}_N)$ and $E_{q,p}(\widehat{\mathfrak{gl}}_N)$
Hitoshi Konno

Editor(s) Hitoshi Konno, Hidetaka Sakai, Junichi Shiraishi, Takao Suzuki, Yasuhiko Yamada

Abstract

We reformulate a central extension of Felder's elliptic quantum group in the FRST formulation as a topological algebra $E_{q,p}(\widehat{\mathfrak{gl}}_N)$ over the ring of formal power series in $p$. We then discuss the isomorphism between $E_{q,p}(\widehat{\mathfrak{gl}}_N)$ and the elliptic algebra $U_{q,p}(\widehat{\mathfrak{gl}}_N)$ of the Drinfeld realization. An evaluation $H$-algebra homomorphism from $U_{q,p}(\widehat{\mathfrak{gl}}_N)$ to a dynamical extension of the quantum affine algebra $U_{q}(\widehat{\mathfrak{gl}}_N)$ resolves the problem into the one discussed by Ding and Frenkel in the trigonometric case. We also provide some useful formulas for the elliptic quantum determinants.

Information

Published: 1 January 2018
First available in Project Euclid: 21 September 2018

zbMATH: 07039308
MathSciNet: MR3837927

Digital Object Identifier: 10.2969/aspm/07610347

Subjects:
Primary: 17B37, 20G42, 81R10, 81R50

Rights: Copyright © 2018 Mathematical Society of Japan

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