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.

11 pages

References in corpus (2)

• Reflection algebras for sl(2) and gl(1|1)
• Diagonalization of infinite transfer matrix of boundary $U_{q,p}(A_{N-1}^{(1)})$ face model

Cited by in corpus (9)

• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• Universal K-matrices for quantum Kac-Moody algebras
• The alternating central extension of the $q$-Onsager algebra
• The alternating presentation of $U_q(\widehat{g{l}_2})$ from Freidel-Maillet algebras
• A conjecture concerning the $q$-Onsager algebra
• 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