Vol. 12, No. 3, 2018

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Elliptic quantum groups and Baxter relations

Huafeng Zhang

Vol. 12 (2018), No. 3, 599–647
Abstract

We introduce a category O of modules over the elliptic quantum group of slN with well-behaved q-character theory. We construct asymptotic modules as analytic continuation of a family of finite-dimensional modules, the Kirillov–Reshetikhin modules. In the Grothendieck ring of this category we prove two types of identities: Generalized Baxter relations in the spirit of Frenkel–Hernandez between finite-dimensional modules and asymptotic modules. Three-term Baxter TQ relations of infinite-dimensional modules.

Keywords
elliptic quantum groups, asymptotic representations, Yang–Baxter equation
Mathematical Subject Classification 2010
Primary: 17B37
Secondary: 17B10, 17B80
Milestones
Received: 29 June 2017
Revised: 17 December 2017
Accepted: 10 March 2018
Published: 12 June 2018
Authors
Huafeng Zhang
Laboratoire Paul Painlevé
Université de Lille
Villeneuve d’Ascq
France