Central extension of the reflection equations and an analog of Miki's formula

TL;DR

This paper introduces two types of centrally extended quantum reflection algebras, provides realizations in terms of Yang-Baxter algebra elements, and proposes a boundary analog of Miki's formula for $U_q(\u2212sl_2)$, offering a free field realization of $O_q(sl_2)$ currents.

Contribution

It presents new centrally extended quantum reflection algebras, their realizations, and an analog of Miki's formula for $U_q(sl_2)$, advancing the understanding of boundary quantum algebras.

Findings

Introduced two types of centrally extended quantum reflection algebras.

Provided realizations in terms of the central extension of the Yang-Baxter algebra.

Proposed a boundary analog of Miki's formula for $U_q(sl_2)$.

Abstract

Two different types of centrally extended quantum reflection algebras are introduced. Realizations in terms of the elements of the central extension of the Yang-Baxter algebra are exhibited. A coaction map is identified. For the special case of $U_q(\hat{sl_2})$, a realization in terms of elements satisfying the Zamolodchikov-Faddeev algebra - a `boundary' analog of Miki's formula - is also proposed, providing a free field realization of $O_q(\hat{sl_2})$ (q-Onsager) currents.