Vol. 12, No. 3, 2018

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Elliptic quantum groups and Baxter relations

Huafeng Zhang

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

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