On tetrahedron type equations associated with $B_3,C_3, F_4$ and $H_3$

Abstract

Tetrahedron equation is a three dimensional analogue of the Yang-Baxter equation. It allows a formulation in terms of the Coxeter group $A_3$. This short note includes miscellaneous remarks on the generalizations along $B_3, C_3, F_4$ and the non-crystallographic Coxeter group $H_3$. 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.