Baxter operators and asymptotic representations
  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 $K_0(\mathcal O)$. 
Giovanni Felder, Huafeng Zhang
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