GENERALIZED QUADRANGLES WITH A REGULAR POINT AND ASSOCIATION SCHEMES

There is a new method of constructing generalized quadrangles (GQs) wh ich is based on covering of nets; all GQs with a regular point can be represented in this way. Here we first construct from a generalized qu adrangle Q with a regular point a four-class association scheme A(Q) c alled in brief geometric. It is then natural to call pseudo-geometric any association scheme A with the same parameters as A(Q). We use eige nvalue techniques and the above method of construction to give a chara cterization of pseudo-geometric association schemes which are geometri c.