On tetrahedron type equations associated with $B$$_3$, $C$$_3$, $F$$_4$ and $H$$_3$ (Combinatorial Representation Theory and Connections with Related Fields)

Abstract

Tetrahedron equation is a three dimensional analogue of the Yang-Baxter equation. It allows a formulation in terms of the Coxeter group A₃. This short note includes miscellaneous remarks on the generalizations along B₃, C₃, F₄ and the non-crystallographic Coxeter group H₃. It is a supplement to the author's talk in the online workshop Combinatorial Representation Theory and Connections with Related Fields at RIMS, Kyoto University in November 2021.