Normalized volumes of configurations related with root systems and complete bipartite graphs. (Q1398266)

Let \(\Gamma\subset \mathbb Z^n\) be one of the root systems \(A_{n-1}, B_n, C_n\) and \(D_n\) and \(\Gamma^+\) be the configuration of all positive roots of \(\Gamma\) and the origin of \(\mathbb R^n\). Gröbner basis theory applied to toric ideals is used to compute the normalized volume of the convex hull of each of the subconfigurations \(B_n^+, C_n^+\) and \(D_n^+\) arising from a complete bipartite graph.