Generalized q -Onsager algebras and dynamical K -matrices

Author： Belliard S.   Fomin V.  

Publisher： IOP Publishing

ISSN： 1751-8121

Source： Journal of Physics A: Mathematical and Theoretical, Vol.45, Iss.2, 2012-01, pp. : 25201-25217

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Abstract

A procedure to construct K-matrices from the generalized q-Onsager algebra &$mathcal O_{q}(widehat{g})$; 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 &$mathcal O_{q}big(a^{(2)}_{2}big)$; and &$mathcal O_{q}big(a^{(1)}_{2}big)$; are treated in detail.

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