Takaaki Nomura (Kyushu University, Japan): Minimum size matrix realization of a homogeneous cone

Among matrix realizations of a homogeneous cone, I will give a one with the minimum size. This realization is given with the help of the oriented graph drawn by the algebraic data of a given homogeneous cone. The formula of this minimum size is written with the graphical terms. The procedure puts the general theory of homogeneous cones considered difficult so far in the black box, so that the access to homogeneous open convex cones becomes easier to non-specialists, I hope.