On connectedness of graphs on Weyl groups of type \(A_ n\) (\(n\geq 4\)). (English) Zbl 0854.20052

Youssef, Samy A.; Hulsurkar, S. G.

Arch. Math., Brno 31, No. 3, 163-170 (1995).

The first author [Graphs on Weyl groups, Ph.D. Thesis, Indian Inst. Technol., Kharagpur (1992)] and the authors [Arch. Math. Brno 29, No. 1-2, 19-23 (1993; Zbl 0798.05029)] have defined and studied a graph structure on Weyl groups using the root system associated with them. In the present paper the authors show that such graphs are connected for Weyl groups of type \(A_n\) (\(n\geq 4\)). The graphs on Weyl groups of type \(A_1\), \(A_2\), \(A_3\) and \(B_2\) are disconnected. The authors conjecture that the graphs on Weyl groups of irreducible root systems are connected except the four types indicated.

Reviewer: V.L.Popov (Moskva)

MSC:

20F55	Reflection and Coxeter groups (group-theoretic aspects)
05C25	Graphs and abstract algebra (groups, rings, fields, etc.)

Keywords:

graphs on Weyl groups; irreducible root systems

Citations:

Zbl 0798.05029