Diagrams for symplectic type configurations

Abstract

In [1] we gave a procedure that associates to each graph Gamma a configuration C(Gamma) of symplectic type. We called this graph "a diagram for the configuration". In the same paper we prove that certain Dynkin-like diagrams (see Example 3 below) define the reduced symplectic configurations Sp(2m,2),O+(2m, 2) and O-(2m,2). In this note, using Hall's classification given in [2], we give diagrams for all symplectic type configurations (Theorem 1 and Remark), As an application we give a characterization of the universal representation for C(Gamma) and prove that our procedure defines the universal representation of C(Gamma).