Abstract
Each orientation on a Dynkin graph
Γ
defines a cone (in a certain real configuration space) which is further divided into chambers. We enumerate the number of chambers for two particular cones, which are called the pricipal
Γ
-cones and are attached to bipartite decompositions of
Γ
, by a use of hook length formulae. We prove that these pricipal cones are characterized by the maximality of the number of chambers in them.