On Connectedness of Graphs on Direct Product of Weyl Groups
نویسندگان
چکیده
In this paper, we have studied the connectedness of the graphs on the direct product of the Weyl groups. We have shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. In particular, we show that the graph on the direct product of the Weyl groups is connected ii the graph on each factor of the direct product is connected. 1. Introduction. In this paper, the connectedness of the graphs on the direct product of the Weyl groups is investigated. It is shown that the number of the connected components of the graph on the direct product of the Weyl groups is equal to the product of the numbers of the connected components of the graphs on the factors of the direct product. From this we deduce that the graph on the direct product of the Weyl groups is connected ii the graph on each factor of the direct product is connected. The graph on Weyl groups has been deened and studied in 1]. The relevant deenitions and the results on the Weyl groups can be found in 2]. We have used the notations given in 3]. We brieey summarize below the required results and the notations. Let E be a xed euclidean space i.e., E is a nite dimensional vector space over real numbers and has a positive deenite symmetric bilinear form (;). Let dimension
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تاریخ انتشار 1995