NONREDUCED EXTENDED AFFINE ROOT SYSTEMS OF NULLITY-3

In 1985 K. Saito [S] introduced the concept of an extended affine root system (EARS). His study of these root systems was motivated by his i nterest in singularities. Later in [AABGP], this notion played an impo rtant role in the study of extended affine Lie algebras. Saito classif ied the EARS's of nullity less than or equal to 2 which have the furth er property that the quotient modulo a ''marking'' is reduced. In [AAB GP], a construction was given of all EARS's, and this was used to give a classification of EARS's of reduced type. However, when tile EARS w as not reduced, the isomorphism problem for the construction is quite difficult and the classification was only done for EARS's with nullity less than or equal to 2. The present paper extends this classificatio n to nullity 3.