Baxter operators and asymptotic representations

Abstract

We introduce a category $\mathcal{O}$ of representations of the elliptic quantum group associated with ${\mathfrak{sl}}_2$ with well-behaved $q$-character theory. We derive separation of variables relations for asymptotic representations in the Grothendieck ring of this category. Baxter $Q$-operators are obtained as transfer matrices for asymptotic representations and obey $TQ$-relations as a consequence of the relations in $K_0(\mathcal{O})$.

arXiv comment16+5 pages

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Cited by in corpus (6)

• Asymptotic Representations of Quantum Affine Superalgebras
• Length-two representations of quantum affine superalgebras and Baxter operators
• Yangians and Baxter's relations
• Elliptic quantum groups and Baxter relations
• Theta series for quantum loop algebras and Yangians
• Jordanian spin chains for twisted strings in $Ad{S}_5\times S^5$