Asymptotic representations of augmented q -Onsager algebra and boundary K -operators related to Baxter Q-operators

Pascal Baseilhac (1) , Zengo Tsuboi (2)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

We consider intertwining relations of the augmented q-Onsager algebra introduced by Ito and Terwilliger, and obtain generic (diagonal) boundary K-operators in terms of the Cartan element of U q (sl 2). These K-operators solve reflection equations. Taking appropriate limits of these K-operators in Verma modules, we derive K-operators for Baxter Q-operators and corresponding reflection equations.

Mots clés: augmented q-Onsager algebra; Baxter Q-operator; K-operator; L-operator; universal R-matrix; reflection equation; asymptotic representation

Domaines: Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]; Algèbres quantiques [math.QA]

Pascal Baseilhac, Zengo Tsuboi. Asymptotic representations of augmented q -Onsager algebra and boundary K -operators related to Baxter Q-operators. Nuclear Physics B, 2018, 929 (April), pp.397-437. ⟨10.1016/j.nuclphysb.2018.02.017⟩. ⟨hal-02154089⟩