Generalized q-Onsager Algebras and Dynamical K-matrices

Abstract

A procedure to construct $K$-matrices from the generalized $q$-Onsager algebra $\cO_{q}(\hat{g})$ is proposed. This procedure extends the intertwiner techniques used to obtain scalar (c-number) solutions of the reflection equation to dynamical (non-c-number) solutions. It shows the relation between soliton non-preserving reflection equations or twisted reflection equations and the generalized $q$-Onsager algebras. These dynamical $K$-matrices are important to quantum integrable models with extra degrees of freedom located at the boundaries: for instance, in the quantum affine Toda field theories on the half-line they yield the boundary amplitudes. As examples, the cases of $\cO_{q}(a^{(2)}_{2})$ and $\cO_{q}(a^{(1)}_{2})$ are treated in details.

References in corpus (5)

• The Universal Askey-Wilson Algebra
• Some algebra related to $P$-and $Q$-polynomial association schemes
• Integrable defects in affine Toda field theory and infinite dimensional representations of quantum groups
• Bethe Ansatz and Bethe Vectors Scalar Products
• Tridiagonal pairs of $q$-Racah type

Cited by in corpus (5)

• The half-infinite XXZ chain in Onsager's approach
• Coideal algebras from twisted Manin triples
• Higher rank classical analogs of the Askey-Wilson algebra from the $s{l}_N$ Onsager algebra
• Drinfeld J Presentation of Twisted Yangians
• Defining relations for quantum symmetric pair coideals of Kac-Moody type