Non-Abelian symmetries of the half-infinite XXZ spin chain

Abstract

The non-Abelian symmetries of the half-infinite XXZ spin chain for all possible types of integrable boundary conditions are classified. For each type of boundary conditions, an analog of the Chevalley-type presentation is given for the corresponding symmetry algebra. In particular, two new algebras arise that are, respectively, generated by the symmetry operators of the model with triangular and special $U_q(g{l}_2)-$invariant integrable boundary conditions.

arXiv comment11 pages

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Cited by in corpus (15)

• The open XXX spin chain in the SoV framework: scalar product of separate states
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• Universal K-matrices for quantum Kac-Moody algebras
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• The alternating central extension of the $q$-Onsager algebra
• The alternating presentation of $U_q(\widehat{g{l}_2})$ from Freidel-Maillet algebras
• FRT presentation of the Onsager algebras
• On Separation of Variables for Reflection Algebras
• A conjecture concerning the $q$-Onsager algebra
• Solutions of the $U_q({\widehat{\mathfrak{sl}}}_N)$ reflection equations
• Integrable boundaries for the q-Hahn process
• Generic triangular solutions of the reflection equation: $U_q(\widehat{s{l}_2})$ case
• Tensor K-matrices for quantum symmetric pairs
• Universal TT- and TQ-relations via centrally extended q-Onsager algebra