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Generalized q-Onsager Algebras and Boundary Affine Toda Field Theories

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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 ≠ 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.

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Authors and Affiliations

  1. Laboratoire de Mathématiques et Physique Théorique, CNRS/UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grammont, 37200, Tours, France

    Pascal Baseilhac

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46, 40126, Bologna, Italy

    Samuel Belliard

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  1. Pascal Baseilhac
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  2. Samuel Belliard
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Baseilhac, P., Belliard, S. Generalized q-Onsager Algebras and Boundary Affine Toda Field Theories. Lett Math Phys 93, 213–228 (2010). https://doi.org/10.1007/s11005-010-0412-6

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