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 $K_0(\mathcal{O})$.

16+5 pages