The central extension of the reflection equations and an analog of Miki’s formula. (English) Zbl 1228.81187
Summary: 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 co-action map is identified. For the special case of \(U_q (\widehat {sl_2})\), 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 \(O_q (\widehat {sl_2})\) (\(q\)-Onsager) currents.
MSC:
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
| 81U15 | Exactly and quasi-solvable systems arising in quantum theory |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
| 81R15 | Operator algebra methods applied to problems in quantum theory |
