Letters in Mathematical Physics

, Volume 93, Issue 3, pp 213–228 | Cite as

Generalized q-Onsager Algebras and Boundary Affine Toda Field Theories



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 ≠ 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 explicitly obtained. As a consequence, based on purely algebraic arguments all integrable (fixed or dynamical) boundary conditions are classified.

Mathematics Subject Classification (2000)

81R50 81R10 81U15 81T40 


q-Onsager algebra quantum group symmetry boundary affine Toda field theory 


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© Springer 2010

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et Physique Théorique, CNRS/UMR 6083, Fédération Denis PoissonUniversité de ToursToursFrance
  2. 2.Istituto Nazionale di Fisica NucleareSezione di BolognaBolognaItaly

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