Generalized q-Onsager algebras and boundary affine Toda field theories

Abstract

Generalizations of the q-Onsager algebra are introduced and studied. In one of the simplest case and q=1, the algebra reduces to the one proposed by Uglov-Ivanov. In the general case and $q\ne 1$, an explicit algebra homomorphism associated with coideal subalgebras of quantum affine Lie algebras (simply and non-simply laced) is exhibited. Boundary (soliton non-preserving) integrable quantum Toda field theories are then considered in light of these results. For the first time, all defining relations for the underlying non-Abelian symmetry algebra are explicitely obtained. As a consequence, based on purely algebraic arguments all integrable (fixed or dynamical) boundary conditions are classified.

13 pages; to appear in Lett. Math. Phys

References in corpus (4)

• A new current algebra and the reflection equation
• Some algebra related to $P$-and $Q$-polynomial association schemes
• Boundary Lax pairs for the $A_n^{(1)}$ Toda field theories
• Tridiagonal pairs of $q$-Racah type

Cited by in corpus (7)

• The $q$-Onsager Algebra and the Universal Askey-Wilson Algebra
• Higher rank classical analogs of the Askey-Wilson algebra from the $s{l}_N$ Onsager algebra
• Reflection algebras for sl(2) and gl(1|1)
• A bispectral q-hypergeometric basis for a class of quantum integrable models
• Higher order relations for ADE-type generalized q-Onsager algebras
• Reflection equation for the N=3 Cremmer-Gervais R-matrix
• The algebra ${\mathcal{A}}_q$, $q-$Onsager algebras and coideal subalgebras: two open problems