Matrix product solutions to the $G_2$ reflection equation

Abstract

We study the $G_2$ reflection equation for the three particles in $1+1$ dimension that undergo a special scattering/reflections described by the Pappus theorem. It is a sixth order equation and serves as a natural $G_2$ analogue of the Yang-Baxter and the reflection equations corresponding to the cubic and the quartic Coxeter relations of type $A$ and $BC$, respectively. We construct matrix product solutions to the $G_2$ reflection equation by exploiting a connection to the representation theory of the quantized coordinate ring $A_q(G_2)$.

19 pages, minor revision

References in corpus (1)

• Matrix product solutions to the reflection equation from three dimensional integrability

Cited by in corpus (1)

• Tetrahedron and 3D reflection equation from PBW bases of the nilpotent subalgebra of quantum superalgebras