Matrix product solutions to the G2 reflection equation. Issue 1 (29th June 2018)

• Record Type: Journal Article
• Authors: Kuniba, Atsuo
• Is Part Of: Journal of integrable systems. Volume 3:Issue 1(2018)
• Publication Date: 2018-06-29
• Subjects: Yang–Baxter equation -- tetrahedron equation -- G2 reflection equation -- quantized coordinate ring; Mathematics -- Periodicals; 510
• DOI: 10.1093/integr/xyy008
• Languages: English
• ISSNs: 2058-5985

Abstract

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 $A_q(G_2)$ . Communicated by: Masatoshi Noumi