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Separation Indices of Small Rank Root Systems

Student: Dariya Kuvshinova

Supervisor: Roman Avdeev

Faculty: Faculty of Computer Science

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Final Grade: 10

Year of Graduation: 2017

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.

Full text (added May 28, 2017)

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