Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators

Abstract

We consider intertwining relations of the augmented $q$-Onsager algebra introduced by Ito and Terwilliger, and obtain generic (diagonal) boundary $K$-operators in terms of the Cartan element of $U_q(s{l}_2)$. These $K$-operators solve reflection equations. Taking appropriate limits of these $K$-operators in Verma modules, we derive $K$-operators for Baxter Q-operators and corresponding reflection equations.

45 pages, v2: universal T- and Q-operators added

References in corpus (8)

• A Shortcut to the Q-Operator
• Hidden Grassmann Structure in the XXZ Model II: Creation Operators
• Hidden Grassmann structure in the XXZ model
• Baxter Q-Operators and Representations of Yangians
• Baxter's Q-operators for supersymmetric spin chains
• The Baxter's Q-operator for the W-algebra $W_N$
• Factorization of R-matrix and Baxter Q-operators for generic sl(N) spin chains
• Drinfeld basis for string-inspired Baxter operators

Cited by in corpus (14)

• Universal K-matrices for quantum Kac-Moody algebras
• QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains
• Non-compact quantum spin chains as integrable stochastic particle processes
• Q-systems with boundary parameters
• The alternating presentation of $U_q(\widehat{g{l}_2})$ from Freidel-Maillet algebras
• A note on $q$-oscillator realizations of $U_q(gl(M|N))$ for Baxter $Q$-operators
• Universal Baxter TQ-relations for open boundary quantum integrable systems
• A Q-operator for open spin chains I: Baxter's TQ relation
• A conjecture concerning the $q$-Onsager algebra
• On diagonal solutions of the reflection equation
• Generic triangular solutions of the reflection equation: $U_q(\widehat{s{l}_2})$ case
• Scaling limit of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$ invariant boundary conditions
• Tensor K-matrices for quantum symmetric pairs
• Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin