SUBFACTORS OF L (F-INFINITY) WITH INDEX 4-COS2-PI/N, N-GREATER-THAN-OR-EQUAL-TO 3

We introduce a noncommutative probability model (in the sense of Voiculescu) for the (reduced) amalgamated free product (L (F(N))X A) A*B, where A subset-or-equal-to B is an inclusion of finite dimensional algebras (with trace). Using this model we prove that A(lambda)n = (L (F(infinity))X A(n)) A(n)*A(n+1) is isomorphic to L (F(infinity)) where A(n) = {e2,..., e(n)}", A(n+1) = {e1,..., e(n)}", (e(i))i being the Jones projections associated to an index value lambda--1. For lambda--1 in Jones' discrete series {4 cos2 pi/m\m greater-than-or-equal-to 3} and n big enough, A(lambda)n is-approximately-equal-to L (F(infinity) is an irreducible subfactor of index lambda--1 in A(lambda)n+1 is-approximately-equal-to L (F(infinity)) of index lambda--1.