ON THE NON-OCCURRENCE OF THE COXETER GRAPHS BETA(2N-FACTORS(1), D(2N+1) AND E(7) AS THE PRINCIPAL GRAPH OF AN INCLUSION OF II(1))

After discussing some preliminaries on the notion of an action of a hy pergroup on a set, we present elementary proofs of the fact that the C oxeter graphs beta2n+1, D2n+1 and E7 do not arise as Jones' principal graph invariant of an inclusion of II(1) factors. (Here, we use the sy mbol beta(n) to denote the graph that is normally denoted by B(n), the reason for this changed terminology being spelt out in the text.)