Universal TT- and TQ-relations are derived for the centrally extended q-Onsager algebra, giving explicit polynomials for local conserved quantities in spin-j chains and new symmetries for special boundaries.
A new (in)finite dimensional algebra for quantum integrable models
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abstract
A new (in)finite dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details. Finite dimensional representations are constructed and mutually commuting quantities - which ensure the integrability of the system - are written in terms of the fundamental generators of the new algebra. Relation with the deformed Dolan-Grady integrable structure recently discovered by one of the authors and Terwilliger's tridiagonal algebras is described. Remarkably, this (in)finite dimensional algebra is a ``$q-$deformed'' analogue of the original Onsager's algebra arising in the planar Ising model. Consequently, it provides a new and alternative algebraic framework for studying massive, as well as conformal, quantum integrable models.
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The alternating central extension U^+_q of U^+_q is isomorphic to U^+_q tensor F[z1,z2,...] via a surjective homomorphism sending alternating generators to alternating elements, with those generators forming a PBW basis.
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Universal TT- and TQ-relations via centrally extended q-Onsager algebra
Universal TT- and TQ-relations are derived for the centrally extended q-Onsager algebra, giving explicit polynomials for local conserved quantities in spin-j chains and new symmetries for special boundaries.
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The alternating central extension for the positive part of $U_q(\widehat{\mathfrak{sl}}_2)$
The alternating central extension U^+_q of U^+_q is isomorphic to U^+_q tensor F[z1,z2,...] via a surjective homomorphism sending alternating generators to alternating elements, with those generators forming a PBW basis.