Complete Decompositions of Coxeter groups orbit products of $A_2, C_2, G_2$ and $H_2$ and some limits for them

Abstract

Orbits of the Weyl reflection groups attached to the simple Lie groups $A_2, C_2, G_2$ and Coxeter group $H_2$ are considered. For each of the groups products of any two orbits are decomposed into the union of the orbits. Results are presented in a single formula for each of the groups. Orbits are considered as functions of two variables and limits for such functions are mentioned.