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 \(K_0(\mathcal {O})\).
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