Matrix product solutions to the reflection equation from three dimensional integrability

Atsuo Kuniba (1) , Vincent Pasquier (2)

1 Institute of Physics, University of Tokyo
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We formulate a quantized reflection equation in which q-boson valued L and K matrices satisfy the reflection equation up to conjugation by a solution to the Isaev–Kulish 3D reflection equation. By forming its n-concatenation along the q-boson Fock space followed by suitable reductions, we construct families of solutions to the reflection equation in a matrix product form connected to the 3D integrability. They involve the quantum R matrices of the antisymmetric tensor representations of and the spin representations of , and .

Domaines: Physique mathématique [math-ph]

Atsuo Kuniba, Vincent Pasquier. Matrix product solutions to the reflection equation from three dimensional integrability. J.Phys.A, 2018, 51 (25), pp.255204. ⟨10.1088/1751-8121/aac3b4⟩. ⟨cea-01748629⟩