Matrix product solution to the reflection equation associated with a coideal subalgebra of $U_q(A_{n-1}^{(1)})$

Abstract

We present a new solution to the reflection equation associated with a coideal subalgebra of $U_q(A_{n-1}^{(1)})$ in the symmetric tensor representations and their dual. Elements of the $K$ matrix are expressed by a matrix product formula involving terminating $q$-hypergeometric series in $q$-boson generators. At $q=0$, our result reproduces a known set-theoretical solution to the reflection equation connected to the crystal base theory.

arXiv comment11 pages, v5: minor corrections

References in corpus (11)

• Quantum symmetric Kac-Moody pairs
• Stochastic $R$ matrix for $U_q(A_n^{(1)})$
• Solutions of the reflection equation for face and vertex models associated with $A_n^{(1)},B_n^{(1)},C_n^{(1)},D_n^{(1)}$ and $A_n^{(2)}$
• Construction of $R$-matrices for symmetric tensor representations related to $U_q(\widehat{s{l}_n})$
• Box-ball system with reflecting end
• Yang-Baxter equation and reflection equations in integrable models
• New non-diagonal solutions to the $a_n^{(1)}$ boundary Yang-Baxter equation
• Surveying the quantum group symmetries of integrable open spin chains
• Matrix product solutions to the reflection equation from three dimensional integrability
• Reflection matrices, coideal subalgebras and generalized Satake diagrams of affine type
• Tetrahedron Equation and Quantum $R$ Matrices for $q$-Oscillator Representations Mixing Particles and Holes

Cited by in corpus (7)

• Universal Baxter TQ-relations for open boundary quantum integrable systems
• Boundary matrices for the higher spin six vertex model
• Integrable boundaries for the q-Hahn process
• Set-theoretical solutions to the reflection equation associated to the quantum affine algebra of type $A_{n-1}^{(1)}$
• Generic triangular solutions of the reflection equation: $U_q(\widehat{s{l}_2})$ case
• $q$-Difference Systems for the Jackson Integral of Symmetric Selberg Type
• Solution to the reflection equation related to the $\iota$quantum group of type AII