On Connectedness of Graphs
نویسندگان
چکیده
A graph structure is deened on the Weyl groups. We show that these graphs are connected for Weyl groups of type An for n 4. 1. Introduction. We have deened a graph structure on Weyl groups through the root system associated with them. The planarity and the other properties of such graphs has been studied elsewhere (1] and 2]). The motivation for these graphs come from the method employed in proving the truth of Verma's conjecture on Weyl's dimension polynomial 3] which arose in connection with the irreducible representations of algebraic Chevalley groups and their Lie algebras. A certain matrix was deened there which imposes a new partial order on Weyl groups. That matrix has been also explored by Chastkofsky 4]. The same matrix is the weighted incidence matrix for our deenition of graphs on Weyl groups. We prove in this paper that such
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