Elliptic quantum groups and Baxter relations

Zhang, Huafeng

doi:10.2140/ant.2018.12.599

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Elliptic quantum groups and Baxter relations

Huafeng Zhang

Vol. 12 (2018), No. 3, 599–647

DOI: 10.2140/ant.2018.12.599

Abstract

We introduce a category $O$ of modules over the elliptic quantum group of ${s l}_{N}$ 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

Vol. 12, No. 3, 2018