Year of Graduation
Separation Indices of Small Rank Root Systems
Applied Mathematics and Information Science
The aim of this paper is to compute exact values of separation indices for irreducible root systems D_4, F_4 and B_5. A finite brute force algorithm that enables one to check whether some subset of Weyl chambers is a separating system is proposed. This algorithm is based on a concept named characteristic set of vectors. For this set, a universal method of construction is proposed. Applying this algorithm, we found separating systems of Weyl chambers for root systems D_4, F_4 and B_5, that implies the following exact values sep(D_4) = 12, sep(F_4) = 5 and sep (B_5) = 10. One of the found separating systems of Weyl chambers of the root system B_5 turned out to be simple enough, so it was possible to generalize it to the case of B_l for an arbitrary l and prove that sep(B_l) = 2l.